<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Karlovich, Alexei Yu.</style></author><author><style face="normal" font="default" size="100%">Karlovich, Yuri I.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Invertibility in Banach algebras of functional operators with non-Carleman shifts</style></title><secondary-title><style face="normal" font="default" size="100%">Ukrains'kyj matematychnyj kongres -- 2001. Pratsi. Sektsiya 11. Funktsional'nyj analiz</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2002</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/oyk/files/13_2002_ukrainian_math_congress-kyiv-01.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">Instytut Matematyky NAN Ukrainy</style></publisher><pub-location><style face="normal" font="default" size="100%">Kyiv</style></pub-location><pages><style face="normal" font="default" size="100%">107-124</style></pages><abstract><style face="normal" font="default" size="100%">&lt;script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'&gt;&lt;/script&gt;&lt;p&gt;We prove the inverse closedness of the Banach algebra \(\mathfrak{A}_p\) of functional operators with non-Carleman shifts, which have only two fixed points, in the Banach algebra of all bounded linear operators on \(L^p\). We suppose that \(1 \le p \le \infty\) and the generators of the algebra \(\mathfrak{A}_p\) have essentially bounded data. An invertibility criterion for functional operators in \(\mathfrak{A}_p\) is obtained in terms of&lt;br /&gt;
the invertibility of a family of discrete operators on \(l^p\). An effective invertibility criterion  is established for binomial difference operators with \(l^\infty\) coefficients on the spaces \(l^p\). Using the reduction to binomial difference operators, we give effective criteria of invertibility  for binomial functional operators on the spaces \(L^p\).&lt;/p&gt;
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