Approximation sequences to operators on Banach spaces: a rich approach

Abstract

AbstractCriteria for the stability of finite sections of a large class of convolution type operators on are obtained. In this class, almost all classical symbols are permitted, namely operators of multiplication with functions in having one‐sided limits or slowly oscillating behavior at infinity and convolution operators (as well as Wiener–Hopf and Hankel operators) with combinations of piecewise continuous, slowly oscillating and almost periodic symbols. We use a simpler and more powerful algebraic technique than all previous works: the application of ‐theory together with the rich sequences concept and localization. Beyond stability we study Fredholm theory in sequence algebras. In particular, formulas for the asymptotic behavior of approximation numbers and Fredholm indices are given.