Functional Analysis and Applications Seminar 

13/11/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building
Pedro A. Santos, Instituto Superior Técnico, Universidade Técnica de Lisboa

Inverse-closedness problems in approximation theory

We are concerned with the applicability of the finite sections method to operators belonging to the closed subalgebra of the algebra of the linear bounded operators acting on $L_p$, generated by operators of multiplication by piecewise continuous functions in $\mathbb{R}$ and operators of convolution by piecewise continuous Fourier multipliers. The usual technique is to introduce a larger algebra of sequences, which contains the special sequences we are interested and the usual operator algebra generated by the operators of multiplication and convolution. There is a direct relationship between the applicability of the finite section method for a given operator and invertibility of the corresponding sequence in this algebra. But, contrarily to the $C^*$ case and Banach analogue for Toeplitz operators, in our case several inverse-closedness problems must be solved.