CINXE.COM

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</style> </head> <body class="page-template-default page page-id-15 wp-custom-logo page-two-column colors-light"> <div id="page" class="site"> <a class="skip-link screen-reader-text" href="#content">Saltar al contenido</a> <header id="masthead" class="site-header" role="banner"> <div class="custom-header"> <div class="custom-header-media"> </div> <div class="site-branding"> <div class="wrap"> <a href="http://blogs.mat.ucm.es/marjim/" class="custom-logo-link" rel="home" itemprop="url"><img width="271" height="250" src="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/cropped-3-2016-07-21-Marca-UCM-logo-negro-3.png" class="custom-logo" alt=" Página personal de Mar Jiménez Sevilla" itemprop="logo" sizes="100vw" /></a> <div class="site-branding-text"> <p class="site-title"><a href="http://blogs.mat.ucm.es/marjim/" rel="home"> Página personal de Mar Jiménez Sevilla</a></p> </div> </div> </div> </div> <div class="navigation-top"> <div class="wrap"> <nav id="site-navigation" class="main-navigation" role="navigation" aria-label="Menú superior"> <button class="menu-toggle" aria-controls="top-menu" aria-expanded="false"> <svg class="icon icon-bars" aria-hidden="true" role="img"> <use href="#icon-bars" xlink:href="#icon-bars"></use> </svg><svg class="icon icon-close" aria-hidden="true" role="img"> <use href="#icon-close" xlink:href="#icon-close"></use> </svg>Menú </button> <div class="menu-menu-principal-container"><ul id="top-menu" class="menu"><li id="menu-item-24" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-home menu-item-24"><a href="http://blogs.mat.ucm.es/marjim/">PORTADA</a></li> <li id="menu-item-22" class="menu-item menu-item-type-post_type menu-item-object-page current-menu-item page_item page-item-15 current_page_item menu-item-22"><a href="http://blogs.mat.ucm.es/marjim/investigacion/">INVESTIGACIÓN</a></li> <li id="menu-item-23" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-23"><a href="http://blogs.mat.ucm.es/marjim/docencia/">DOCENCIA</a></li> </ul></div> </nav> </div> </div> </header> <div class="site-content-contain"> <div id="content" class="site-content"> <div class="wrap"> <div id="primary" class="content-area"> <main id="main" class="site-main" role="main"> <article id="post-15" class="post-15 page type-page status-publish hentry"> <header class="entry-header"> <h1 class="entry-title">INVESTIGACIÓN</h1> </header> <div class="entry-content"> <p style="text-align: left" align="center"><strong><span style="color: #008000">RESEARCH INTERESTS</span></strong></p> <p><span style="color: #000000">My general research interest is in Geometry of infinite dimensional Banachspaces. This research falls within the field of Functional Analysis. My current research plans are concentrated within the following general areas:</span></p> <ul> <li><span style="color: #000000">Renormings of Banachspaces. A central problem within the Banach space theory is that of knowing if a given space has or has not norms (i.e. admits or not renormings) with good smoothness and/or convexity properties. This is important because isomorphic properties can be deduced from this information.</span></li> <li><span style="color: #000000">Norm attaining mappings. The structure of the so-called Bishop-Phelps set on a given Banachspace X (i.e, the set of norm attaining functionalson X) is of interest in my research. Within this subject, there are very nice, interesting problems we are attempting. Some of them are related to the study of those Banachspaces where a «generalization» of the Bishop-Phelps Theorem holds, namely, the density of the set of norm attaining operators or multilinear mappings or polynomials.</span></li> <li><span style="color: #000000">The metric space (H(X),h) of all bounded, closed and convex sets of a Banach space X with the Hausdorff metric. One of the most important reasons why we are interested in this space is because many properties within the theory of Banach spaces can be reformulated in the following way: «every subset of H(X) satisfies a given condition». This is the case, for instance, of the well-known Radon Nikodym property (geometrical version). Thus, where X does not possess such property, it is interesting to study the topological aspects of the subset of H(X) which is still satisfying the given condition.</span></li> <li><span style="color: #000000">Smooth functions and smooth bump functions. The study of the existence of smooth (Gâteaux,Fréchet, etc…) bump functions and its properties on certain Banach spaces plays a central role within the geometry of Banachspaces. We are mainly interested in: (1) the range and the size of the set of gradients of smooth bump functions and more general smooth functions; (2) properties of approximation such as approximation of Lipschitz functions by $C^1$-smooth and Lipschitz functions; (3) properties of extensions such as $C^1$-smooth extensions of functions defined on a closed subset of a Banach space X.</span></li> <li><span style="color: #000000">Banach-Finsler Manifolds. The study of smoothness properties on Banach-Finsler manifolds such as smooth approximation of functions, non-smooth analysis and Hamilton-Jacobi equations on Banach-Finsler manifolds.</span></li> <li>Operator ranges: Subspaces of Banach spaces that are the range of an operator between two Banach spaces. This kind of subspaces is of relevant importance and are related to the separable quotient problem. Operators between Banach spaces with a prescribed behaviour with respect to a countable union of infinite codimensional operator ranges. Quasicomplemented subspaces.</li> </ul> <hr /> <h1 style="text-align: left" align="center"><strong><span style="color: #008000">PUBLICATIONS</span></strong></h1> <p><a href="https://www.sciencedirect.com/science/article/pii/S0022123624001769?dgcid=rss_sd_all"><strong>Approximate Morse-Sard Type results for non-separable Banach spaces,</strong></a></p> <p><span style="font-size: 1rem">D. Azagra, M. García-Bravo, M. Jiménez-Sevilla, </span></p> <p><a href="https://www.sciencedirect.com/science/article/pii/S0022123624001769?via%3Dihub"><span style="font-size: 1rem">Journal of Functional Analysis <span class="anchor-text-container"><span class="anchor-text">Volume 287, Issue 4</span></span>, 15 August 2024, 110488</span></a></p> <p><a href="https://www.icmat.es/RT/2024/LSAA/slides/Jimenez.pdf"><span style="color: #008000"><strong>TALK</strong> at the ICMAT (Madrid), Workshop on Banach spaces and Banach lattices 2024. </span></a></p> <p> </p> <p><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2024/01/WeakStar-Separable.pdf"><strong>Operator ranges in Banach spaces with weak star separable dual.</strong></a></p> <p>M. Jimenez-Sevilla, Sebastián Lajara.</p> <p><a href="https://www.sciencedirect.com/science/article/pii/S0022247X23008843"> <em>J. Math. Anal. Appl.</em> 531 (2024), no. 2, part 2, Paper No. 127881, 21 pp.</a></p> <p> </p> <p><a href="https://www.researchgate.net/publication/368225761"><strong>Quasicomplemented subspaces of Banach spaces and separable quotients.</strong></a></p> <p>M. Jiménez-Sevilla, Sebastián Lajara.</p> <p><a href="https://link.springer.com/article/10.1007/s00025-023-02022-1"><em>Results Math.</em> 78 (2023), no. 6, Paper No. 244, 24 pp.</a></p> <p> </p> <p><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2022/06/OpRanges.pdf"><strong>Operator ranges and endomorphisms with a prescribed behaviour on Banach Spaces.</strong></a></p> <p>M. Jiménez-Sevilla, Sebastián Lajara.</p> <p><a href="https://link.springer.com/article/10.1007/s13398-022-01368-5"><em>Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM</em> 117 (2023), no. 1, Paper No. 33, 29 pp.</a></p> <p><a href="https://www.icmat.es/congresos/2022/BSBL/slides/Jimenez-Sevilla.pdf"><span style="color: #008000"><strong>TALK</strong> at the ICMAT (Madrid), Workshop on Banach spaces and Banach lattices II (2022)</span></a></p> <p> </p> <p><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/08/Tilings.pdf"><strong>Normal and starlike tilings in separable Banach spaces.</strong></a></p> <p>R. Deville, M. Jiménez-Sevilla,</p> <p><a href="https://www.sciencedirect.com/science/article/pii/S0022247X21001955?casa_token=3cW_80D3vGoAAAAA:OaUps2uUJzPH89-Yq3zazUdPL36G6QVUY72s-WWCZ8xsMpk9Eu62z4szvMt6LqfssnYzkCa_">Journal of Mathematical Analysis and Applications, 500 (2021) no. 2, 125116.</a></p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/H-J-Finsler.pdf">A class of Hamilton-Jacobi equations on Banach-Finsler manifolds.</a></strong></p> <p>J. A. Jaramillo, M. Jiménez-Sevilla, J. L. Ródenas and L. Sánchez-González,<br /> Nonlinear Analysis: Theory, Methods and Applications, 113(2015), 159–179.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/BS.pdf">Cha</a></strong><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/BS.pdf">racterization of a Banach-Finsler manifold in terms of the algebras of smooth functions</a></strong><strong><a href="http://matnfs.mat.ucm.es/~marjim/papers/LFCbumps.pdf">.</a></strong></p> <p>J. A. Jaramillo, M. Jiménez-Sevilla and Luis Sánchez-González,<br /> Proceedings of the American Math. Soc. 142 (2014) no. 3, 1075–1087.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/SmoothExtVectorV.pdf">On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces.</a></strong></p> <p>M. Jiménez-Sevilla and Luis Sánchez-González,<br /> Math. Ann. 355 (2013), 1201-1219.</p> <p><span style="color: #008000"><strong><a style="color: #008000" href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2024/06/2024_05_11_Corrigendum.pdf">Corrigendum to «On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces».</a></strong></span></p> <p><span style="color: #008000">Mar Jiménez-Sevilla</span></p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/Banach-Finsler.pdf">On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach-Finsler Manifolds.</a></strong></p> <p>M. Jiménez-Sevilla and Luis Sánchez-González.<br /> Nonlinear Analysis: Theory, Methods & Applications,74 (2011), 3487-3500.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/Extens.pdf">Smooth extensions of functions on a certain class of non-separable Banach spaces</a></strong><strong><a href="http://matnfs.mat.ucm.es/~marjim/papers/LFCbumps.pdf">.</a></strong></p> <p>M. Jiménez-Sevilla and Luis Sánchez-González, Journal of Mathematical Analysis and Applications, 378 (2011), 173-183.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/LFCbumps.pdf">LFC bumps on separable Banach spaces</a></strong><strong><a href="http://matnfs.mat.ucm.es/~marjim/papers/LFCbumps.pdf">. </a></strong></p> <p>M. Jiménez-Sevilla and Luis Sánchez-González,<br /> Journal of Mathematical Analysis and Applications, 365 (2010), 315-319.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/NoteAnalytic.pdf">A note on the range of the derivatives of analytic approximations of uniformly continuous functions on c0</a></strong><a href="http://matnfs.mat.ucm.es/~marjim/papers/RangeAnalityc.pdf"><strong>.</strong></a></p> <p>M. Jiménez-Sevilla<br /> Journal of Mathematical Analysis and Applications 348 (2008), n. 2, 573-580.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/GMLS.pdf">Generalized motion of level sets by functions of their curvatures on Riemannian manifolds.</a></strong></p> <p>D. Azagra, M. Jiménez-Sevilla and F. Macià,<br /> Cal. Var. Partial Differential Equations 33 (2008), n. 2, 133-167.</p> <p> </p> <p><strong>Approximations by smooth functions with no critical points on separable Banach spaces.</strong></p> <p>D. Azagra and M. Jiménez-Sevilla,<br /> Journal of Functional Analysis 242 (1) (2007), 1-36.</p> <p> </p> <p><strong>Exact filling of figures with the derivatives of smooth mappings between Banach spaces.</strong></p> <p>D. Azagra, M.Fabian, M. Jiménez-Sevilla<br /> Canadian Mathematical Bulletin 48, no. 4 (2005), 481-499.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/SurveyMazur.pdf">Intersection of closed balls and geometry of Banach spaces (Survey).</a></strong></p> <p>Antonio S. Granero, M. Jiménez-Sevilla, Jose Pedro Moreno<strong><br /> </strong>Extracta Mathematicae 19 (num. 2) (2004), 55-92.</p> <p> </p> <p><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/GJMMP.pdf"><strong>On the Kunen-Shelah properties Banach spaces.</strong></a></p> <p>A. S. Granero, Mar Jiménez-Sevilla, J. P. Moreno, A. Montesinos y A. Plichko<br /> Studia Mathematica 157 (no. 2), (2003), 97-120.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/ADJ5.pdf">On the Range of the derivatives of a smooth function between Banach spaces.</a></strong></p> <p>D. Azagra, R.Deville, M. Jiménez-Sevilla<br /> Math. Proc. Cambdrige Philosophical Society 134 (num. 1), (2003), 163-185.</p> <p> </p> <p><strong>On the size of the sets of gradients of bump functions and starlike bodies on the Hilbert space.</strong></p> <p>D. Azagra, M. Jiménez-Sevilla<br /> Bull. Soc. Math. Franc. 130, (2002), 337-347.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/survey.pdf">Geometrical and topological properties of bumps and starlike bodies in Banach spaces.</a></strong></p> <p>D. Azagra, M. Jiménez-Sevilla<br /> Extracta Mathematicae 17(2), (2002), 151-2002.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/companion.pdf">Antiproximinal norms in Banach spaces</a></strong></p> <p>J. M. Borwein, M. Jiménez-Sevilla, J. P. Moreno<br /> Journal of Approximation Theory 114, (2002), 57-69.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/omega5.pdf">On w-independence and the Kunen-Shelah property</a></strong></p> <p>A. S. Granero, M. Jiménez-Sevilla, J. P. Moreno<br /> Proc. Edinburgh Math. Soc. 45, (2002), 391-395.</p> <p> </p> <p><strong>Complementation and embbedings of co(I) in Banach spaces</strong></p> <p>S. A. Argiros, J. F. Castillo, A. S. Granero, M. Jiménez-Sevilla y J. P. Moreno<br /> Proceedings of the London Mathematical Society 85(3), (2002), 742-768.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/rolles.pdf">The failure of Rolle’s theorem in infinite dimensional Banach spaces</a></strong></p> <p>D.Azagra, M. Jiménez-Sevilla<br /> Journal of Functional Analysis, 182(2001), 207-226.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/porosity1.pdf">A constant of porosity for convex bodies</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> Illinois Journal of Mathematics 45 (2001), 1061-1071.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/notapor.pdf">A note on porosity and Mazur intersection property</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> Mathematika 47 (2000), 267-272.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/jw7.pdf">On the non-separable subspaces J(\eta) and C[1,\eta]</a></strong></p> <p>Antonio S. Granero, M. Jiménez-Sevilla, J.P. Moreno<br /> Mathematishe Nachrichten 221 (2001), 75-85.</p> <p> </p> <p><strong>Mazur intersection properties and differentiability of convex functions in Banach spaces</strong></p> <p>P. S. Georgiev, Antonio S. Granero, M. Jiménez-Sevilla, J.P. Moreno<br /> J. London Math. Soc. (2) 61 (2000) no. 2, 531-542</p> <p> </p> <p><strong>Sequential continuity in the ball topology of a Banach space</strong></p> <p>Antonio S. Granero, M. Jiménez-Sevilla, J.P. Moreno,<br /> Indagationes Mathematicae 10 (3) (1999), 423-435</p> <p> </p> <p><strong>Geometry of Banach spaces with property beta </strong></p> <p>Antonio S. Granero, M. Jiménez-Sevilla, J.P. Moreno,<br /> Israel Journal of Mathematics 111 (1999), 263-273</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/naf.pdf">A note on norm attaining functionals</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> Proc. Am. Math. Soc. 126 (1998), 1989-1997</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/convex.pdf">Convex sets on Banach spaces and a problem of Rolewicz</a></strong></p> <p>Antonio S. Granero, M. Jiménez-Sevilla, J. P. Moreno<br /> Studia Mathematica 129 (1) (1998), 19-29</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/multilinear.pdf">Norm attaining multilinear forms and polynomials on predual of Lorentz sequence spaces</a></strong></p> <p>Rafael Payá, M. Jiménez-Sevilla<br /> Studia Mathematica 127 (2) (1998), 99-112.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/renorming.pdf">Renorming Banach spaces with the Mazur intersections Property</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> Journal Functional Analysis 144 (2) (1997), 486-504</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/denseness.pdf">On denseness of certain norms in Banach spaces</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> Bull. Austral. Math. Soc. 54 (1996), 183-196.</p> <p> </p> <p><strong><a href="http://blogs.mat.ucm.es/marjim/wp-content/uploads/sites/56/2020/07/MazurR.pdf">The Mazur intersection property and Asplund spaces</a></strong></p> <p>M. Jiménez-Sevilla, J.P. Moreno<br /> C. R. Acad.Sci. Paris, t. 321, Série I, p. 1219-1223, (1995).</p> <hr /> <h1><strong><span style="color: #008000">TESIS (PhD DISSERTATION)</span></strong></h1> <p>Tesis realizada:<strong> Algunos problemas relacionados con la geometría de los espacios de Banach</strong></p> <p>Tesina realizada:<strong> <a href="http://www.mat.ucm.es/~marjim/convexjim.pdf">Funciones convexas en espacios de Banach</a> </strong></p> </div> </article> </main> </div> </div> </div> <footer id="colophon" class="site-footer" role="contentinfo"> <div class="wrap"> <div class="site-info"> <a href="https://es.wordpress.org/" class="imprint"> Funciona gracias a WordPress </a> </div> </div> </footer> </div> </div> <aside id="moove_gdpr_cookie_info_bar" class="moove-gdpr-info-bar-hidden moove-gdpr-align-center moove-gdpr-dark-scheme gdpr_infobar_postion_bottom" role="note" aria-label="Banner de cookies RGPD"> <div class="moove-gdpr-info-bar-container"> <div class="moove-gdpr-info-bar-content"> <div class="moove-gdpr-cookie-notice"> <p>Esta web utiliza cookies para ofrecerte la mejor experiencia de navegación posible.</p><p>Descubre más o ajusta tus <span data-href="#moove_gdpr_cookie_modal" class="change-settings-button">ajustes</span>.</p></div>  <div class="moove-gdpr-button-holder"> <button class="mgbutton moove-gdpr-infobar-allow-all">Aceptar</button> </div>  </div>  </div>  </aside>  <script type='text/javascript'> /* <![CDATA[ */ var wpcf7 = {"apiSettings":{"root":"http:\/\/blogs.mat.ucm.es\/marjim\/wp-json\/contact-form-7\/v1","namespace":"contact-form-7\/v1"}}; 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