@inbook {7468, title = {Invertibility in Banach algebras of functional operators with non-Carleman shifts}, booktitle = {Ukrains{\textquoteright}kyj matematychnyj kongres -- 2001. Pratsi. Sektsiya 11. Funktsional{\textquoteright}nyj analiz}, year = {2002}, pages = {107-124}, publisher = {Instytut Matematyky NAN Ukrainy}, organization = {Instytut Matematyky NAN Ukrainy}, address = {Kyiv}, abstract = {

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
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 \(L^p\).

}, attachments = {https://docentes.fct.unl.pt/sites/default/files/oyk/files/13_2002_ukrainian_math_congress-kyiv-01.pdf}, author = {Karlovich, Alexei Yu. and Karlovich, Yuri I.} }