19/04/2002, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
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 of
functional operators with non-Carleman shifts, which have only two
fixed points, in the Banach algebra of all bounded linear operators
on . We suppose that the generators of the algebra have
essentially bounded data. An invertibility criterion for functional
operators in is obtained in terms of the invertibility of a
family of discrete operators on . An effective invertibility
criterion is established for binomial difference operators with
bounded coefficients on the spaces . Using the reduction to
binomial difference operators, we give effective criteria of
invertibility for binomial functional operators on the spaces
.
These results are obtained in collaboration with Yuri
Karlovich.