Functional Analysis and Applications Seminar 

19/04/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Instituto Superior Técnico, U.T.L.

Invertibility in Banach Algebras of Functional Operators withNon-Carleman Shifts

We prove the inverse closedness of the Banach algebra $A$ 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 the generators of the algebra $A$ have essentially bounded data. An invertibility criterion for functional operators in $A$ 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 bounded 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 $L^p$.

These results are obtained in collaboration with Yuri Karlovich.