Functional Analysis and Applications Seminar 

04/07/2014, 14:30 — 15:30 — Room P3.10, Mathematics Building
Helena Mascarenhas, Instituto Superior Técnico

Variable-coefficient Toeplitz matrices and Singular Values

In this talk we describe asymptotic spectral properties of sequences of variable-coefficient Toeplitz matrices. These sequences, $A_N (a)$, with the symbol $a$ being in a Wiener type algebra and defined on a finite cylinder, widely generalizes the sequences of finite sections of a Toeplitz operator. We prove that if a does not vanish, then the singular values of $A_N (a)$ have the $k$-splliting property, which means that, there exist an integer $k$ such that, for $N$ large enough, the first $k$th-singular values of $A_N(a)$ converge to zero as $N$ goes to infinity while the others are bounded away from zero, with $k$ equals the sum of the  kernel dimension of two Toeplitz operators.

The talk is based on joint work with B. Silbermann.