Document Zbl 1524.47019

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Methods Appl. Sci.</a> <a href="/?q=in%3A335900" title="Articles in this Issue">37, No. 14, 2135-2149 (2014)</a>. </div> <div class="abstract"><div class="pre">Summary: In this paper, we deal with the $M$-essential spectra of unbounded linear operators in Banach spaces where some generalizations of earlier work are given. Furthermore, we give an application from transport theory.<br class="zbmathjax-paragraph">Copyright © 2013 John Wiley & Sons, Ltd.</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6353370">Cited in <strong>11</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A56" title="MSC2020">47A56</a> </td> <td class="space"> Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A08" title="MSC2020">47A08</a> </td> <td class="space"> Operator matrices </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47B01" title="MSC2020">47B01</a> </td> <td class="space"> Operators on Banach spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A10" title="MSC2020">47A10</a> </td> <td class="space"> Spectrum, resolvent </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A53" title="MSC2020">47A53</a> </td> <td class="space"> (Semi-) Fredholm operators; index theories </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A55" title="MSC2020">47A55</a> </td> <td class="space"> Perturbation theory of linear operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aoperator+matrix">operator matrix</a>; <a href="/?q=ut%3Aclosure">closure</a>; <a href="/?q=ut%3A%24M%24-essential+spectrum">$M$-essential spectrum</a>; <a href="/?q=ut%3Atransport+operator">transport operator</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1524.47019" data-ciurl="/ci/06353370" data-biburl="/bibtex/06353370.bib" data-amsurl="/amsrefs/06353370.bib" data-xmlurl="/xml/06353370.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06353370.pdf" title="Zbl 1524.47019 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/mma.2961" aria-label="DOI for “On the M-essential spectra of two-group transport equations”" title="10.1002/mma.2961">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Markus, AS, Introduction to the Spectral Theory of Polynomial Operator Pencils, 1988, American Mathematical Society: Providence · <a href="/0678.47005" class="nowrap">Zbl 0678.47005</a></td> </tr><tr> <td>[2]</td> <td class="space">Shkalikov, AA; Tretter, C., Spectral analysis for linear pencils N − λP of ordinary differential operators, Mathematische Nachrichten, 179, 275-305, 1996 · <a href="/0862.34058" class="nowrap">Zbl 0862.34058</a></td> </tr><tr> <td>[3]</td> <td class="space">Nagel, R., Well‐posedness and positivity for systems of linear evolution equations, Conferenze del Seminario di Matematica dell’Università di Bari, 203, 29, 1985 · <a href="/0596.35059" class="nowrap">Zbl 0596.35059</a></td> </tr><tr> <td>[4]</td> <td class="space">Nagel, R., Towards a matrix theory for unbounded operator matrices, Mathematishe Zeitschrift, 1, 57-68, 1989 · <a href="/0672.47001" class="nowrap">Zbl 0672.47001</a></td> </tr><tr> <td>[5]</td> <td class="space">Nagel, R., The spectrum of unbounded operator matrices with non‐diagonal domain, Journal of Functional Analysis, 89, 291-302, 1990 · <a href="/0704.47001" class="nowrap">Zbl 0704.47001</a></td> </tr><tr> <td>[6]</td> <td class="space">Nagel, R., Characteristic equations for the spectrum of generators, Annali della Scuola Normale Superiore di Pisa ‐ Classe di Scienze, 24, 703-717, 1997 · <a href="/0912.47023" class="nowrap">Zbl 0912.47023</a></td> </tr><tr> <td>[7]</td> <td class="space">Batkai, A.; Binding, P.; Dijksma, A.; Hryniv, R.; Langer, H., Spectral problems for operator matrices, Mathematische Nachrichten, 278, 1408-1429, 2005 · <a href="/1103.47001" class="nowrap">Zbl 1103.47001</a></td> </tr><tr> <td>[8]</td> <td class="space">Moalla, N.; Dammak, M.; Jeribi, A., Essential spectra of some matrix operators and application to two‐group transport operators with general boundary conditions, Journal of Mathematical Analysis and Applications, 2, 323, 1071-1090, 2006 · <a href="/1108.47014" class="nowrap">Zbl 1108.47014</a></td> </tr><tr> <td>[9]</td> <td class="space">Jeribi, A.; Walha, I., Gustafson, Weidmann, Kato, Wolf, Schechter and Browder essential spectra of some matrix operator and application to a two‐group transport equations, Mathematische Nachrichten, 284, 1, 67-86, 2011 · <a href="/1217.15013" class="nowrap">Zbl 1217.15013</a></td> </tr><tr> <td>[10]</td> <td class="space">Atkinson, FV; Langer, H.; Mennicken, R.; Shkalikov, AA, The essential spectrum of some matrix operators, Mathematische Nachrichten, 167, 5-20, 1994 · <a href="/0831.47001" class="nowrap">Zbl 0831.47001</a></td> </tr><tr> <td>[11]</td> <td class="space">Charfi, S.; 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