Functional Analysis and Applications Seminar 

22/06/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building
Helena Mascarenhas, Instituto Superior Técnico, UT Lisboa

Spectral approximation and index for bidimensional convolution type operators on cones

We consider an algebra of operator sequences containing, among others, the approximation sequences to convolution type operators on cones acting on the Lebesgue space. To each operator sequence $A_n$ we associate a family of operators $W_x(A_n)$ parametrized by $x$ in some index set. When all $W_x(A_n)$ are Fredholm, the so-called approximation numbers of $A_n$ have the $\alpha$ splitting property with $\alpha$ being the sum of the kernel dimensions of $W_x(A_n)$. Moreover, the sum of the indices of $W_x(A_n)$ is zero. We also show that the index of some composed convolution-like operators is zero. Results on the convergence of the pseudospectrum, norms of inverses and condition numbers are also obtained. This talk is based on joint work with B. Silbermann.