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REVIEWEDtruefalse10011414false10011414true1661-82541661-8262JournalFOREIGN133132513601325362019Let T be a bounded linear operator on a Hilbert space H such thatalpha[T*,T]:=Sigma(infinity)(n=0)alpha(nTTn)-T-*n >= 0,where alpha(t)=Sigma(infinity)(n=0)alpha(n)t(n) is a suitable analytic function in the unit disc D with real coefficients. We prove that if alpha(t)=(1-t)(alpha) over tilde (t), where (alpha) over tilde has no zeros in [0,1], then T is similar to a contraction. Operators of this type have been investigated by Agler, Muller, Olofsson, Pott and others, however, we treat cases where their techniques do not apply. We write down an explicit Nagy-Foias type model of an operator in this class and discuss its usual consequences (completeness of eigenfunctions, similarity to a normal operator, etc.). We also show that the limits of parallel to T(n)h parallel to as n -> infinity, h is an element of H, do not exist in general, but do exist if an additional assumption on alpha is imposed. Our approach is based on a factorization lemma for certain weighted Wiener algebras.2019truetruetruefalsefalseNONE2022-07-29false00000000000022Q2falsefalsefalsefalse14020trueLanguage10002
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<div class="JournalArticle Publication short-list"> <div class="authors"> <span class="author-name" > Bello-Burguet, Glenier </span> <span class="author-type"> </span> ; <span class="author-name" > Yakubovich, Dmitry ✉ </span> <span class="author-type"> </span> </div ><div class="title"><a href="/gui2/?mode=browse¶ms=publication;30957253" mtid="30957253" target="_blank">Operator Inequalities Implying Similarity to a Contraction</a></div> <div class="pub-info"> <span class="journal-title">COMPLEX ANALYSIS AND OPERATOR THEORY</span> <span class="journal-volume">13</span> : <span class="journal-issue">3</span> <span class="page"> pp. 1325-1360. , 36 p. </span> <span class="year">(2019)</span> </div> <div class="pub-end"><div class="identifier-list"> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s11785-018-0864-8" target="_blank" href="https://doi.org/10.1007%2Fs11785-018-0864-8"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000466779600035" target="_blank" href="http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=CustomerName&SrcApp=CustomerName&DestLinkType=FullRecord&KeyUT=000466779600035&DestApp=WOS"> WoS </a> </span> </span> </div> <div class="short-pub-prop-list"> <span class="short-pub-mtid"> Közlemény:30957253 </span> <span class="status-holder"><span class="status-data status-VALIDATED"> Egyeztetett </span></span> <span class="pub-core"> Idéző </span> <span class="pub-type">Folyóiratcikk (Szakcikk ) </span> <!-- && !record.category.scientific --> <span class="pub-category">Tudományos</span> </div> </div> </div><div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" >Bello-Burguet Glenier </span> ; <span class="author-name" >Yakubovich Dmitry ✉ </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse¶ms=publication;30957253" target="_blank">Operator Inequalities Implying Similarity to a Contraction</a></div> <div> <span class="journal-title">COMPLEX ANALYSIS AND OPERATOR THEORY</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1661-8254">1661-8254</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1661-8262">1661-8262</a>)</span>: <span class="journal-volume">13</span> <span class="journal-issue">3</span> <span class="page"> pp 1325-1360 </span> <span class="year">(2019)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s11785-018-0864-8" target="_blank" href="https://doi.org/10.1007%2Fs11785-018-0864-8"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000466779600035" target="_blank" href="http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=CustomerName&SrcApp=CustomerName&DestLinkType=FullRecord&KeyUT=000466779600035&DestApp=WOS"> WoS </a> </span> </span> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;30957253&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 2 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 30957253</span> | <span class="status-data status-VALIDATED"> Egyeztetett </span> Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">WoS-XML</span> </div> <div class="lastModified">Utolsó módosítás: 2019.12.05. 22:58 WoS admin-2 -1 (WoS import 3, admin) </div> </div></div>