On contractive and convergence properties of a class of truncated operators represented through Schauder bases with applications
type: Item
instance of: scholarly article
title: On contractive and convergence properties of a class of truncated operators represented through Schauder bases with applications
zbMATH Open document ID: 1325.47098
published in: Indagationes Mathematicae. New Series
publication date: 2015-03-23T00:00:00Z
review text: Let \((X,d)\) be a separable complete linear metric space and let \(\{e_n\}_{n=1}^{\infty}\subset X\) be a Schauder basis, that is, the representation \[ x=\sum_{n=1}^{\infty} x_i e_i, \] is unique, for all \(x\in X\). By considering the truncated operators represented through the Schauder basis \(\{e_n\}_{n=1}^{\infty}\subset X\), \(P_m: X\rightarrow X_m\), defined by \[ [x]_m:=P_m x=\sum_{i=1}^{m} x_i e_i, \] the author investigates the relationships between the fixed points of asymptotically contractive operators and their obtained truncations of the expansions of such operators by using Schauder bases. The problem is considered on complete linear metric spaces, in general, and in separable Hilbert spaces in particular. Two illustrative worked examples are given.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6418466
zbMATH Keywords: separable complete linear metric space
zbMATH Keywords: Schauder basis
zbMATH Keywords: expansion
zbMATH Keywords: truncated operator
zbMATH Keywords: asymptotically contractive operator
zbMATH Keywords: fixed point
zbMATH Keywords: homogeneous and translation-invariant metric
zbMATH Keywords: approximate operators
zbMATH Keywords: contractive operators
zbMATH Keywords: discretization-oriented problems
Wikidata QID: Q57674780
author: M. De la Sen
reviewed by: Vasile Berinde
MaRDI profile type: Publication
full work available at URL: j.indag.2015.01.003
OpenAlex ID: W2068991465
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DOI: 10.1016/J.INDAG.2015.01.003
description: scientific article; zbMATH DE number 6418466