03/05/2002, 14:00 — 15:00 — Room P3.10, Mathematics Building
Maria Amélia Bastos, Instituto Superior Técnico, U.T.L.
Fredholm Theory in an Algebra Generated by OperatorswithOscillating
Symbols and the Cauchy Singular Operator
In this talk we deal with a Fredholm theory in the algebra
generated by operators with oscillating symbols and the Cauchy
singular operator as a subalgebra of bounded linear operators in
(-vector) Lebesgue spaces.
In the first part of the talk, using the limit operator theory,
a necessary Fredholmness condition for any operator in is
established and, from one of the local principles, sufficient
Fredholmness conditions for some elements in this algebra are
obtained. A Fredholm criterion for Toeplitz operators with matrix
symbols in the algebra generated by slowly oscillating
and semi-almost periodic matrix functions on is
established as a consequence.
In the second part, using the notion of harmonic extension, an
index theory for Fredholm Toeplitz operators whose generating
functions belong to the algebra is developed. The most
relevant result is obtained by reducing to Toeplitz operators whose
generating functions belong to the space of semi-almost periodic
matrix functions.
This talk is based on common work with Y. Karlovich and B.
Silbermann.