Contractive properties of truncated operators through Schauder bases with some applicationsc

Abstract

This paper investigates the relations between the fixed points of asymptotically contractive operators defined on complete liner metric spaces, in general, and in separable Hilbert spaces in particular and their obtained truncations of the expansions of such operators by using Schauder bases. The truncation used to expand the approximated operators is seen to be specifically relevant for the case when infinite-dimensional Hilbert spaces ate truncated by finite-dimensional ones. The study is of interest in operator discretization-oriented problems which are approximated by truncated operator representations.