On contractive and convergence properties of a class of truncated operators represented through Schauder bases with applications

摘要

This paper investigates the relations between the fixed points of asymptotically contractive operators defined on complete linear 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 are truncated by finite-dimensional ones. The discussion of the situation when the fixed points remain unaltered under the mentioned truncations is also highlighted in the formalism. The study is of interest in operator discretization-oriented problems which are approximated by truncated operator representations. Two illustrative worked examples are given. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.