Operators on spaces of bounded vector-valued continuous functions with strict topologies
type: Item
instance of: scholarly article
title: Operators on spaces of bounded vector-valued continuous functions with strict topologies
zbMATH Open document ID: 1343.46041
DOI: 10.1155/2015/407521
author: Marian Nowak
published in: Journal of Function Spaces
publication date: 2015-08-20T00:00:00Z
review text: Summary: Let \(X\) be a completely regular Hausdorff space, and let \((E,\|\cdot\|_E)\) and \((F,\|\cdot\|_F)\) be Banach spaces. Let \(C_b(X,E)\) be the space of all \(E\)-valued bounded, continuous functions defined on \(X\), equipped with the strict topologies \(\beta_z\), where \(z= \sigma,p,\tau,t\). General integral representation theorems of \((\beta_z,\|\cdot\|_F)\)-continuous linear operators \(T: C_b(X,E)\to F\) with respect to the corresponding operator-valued measures are established. Strongly bounded and \((\beta_z,\|\cdot\|_F)\)-contiguous operators \(T: C_b(X,E)\to F\) are studied. We extend to ``the completely regular setting'' some classical results concerning operators on the spaces \(C(X,E)\) and \(C_0(X,E)\), where \(X\) is a compact or a locally compact space.
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 6474205
zbMATH Keywords: strict topologies
zbMATH Keywords: integral representation
zbMATH Keywords: operator-valued measures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/407521
OpenAlex ID: W2044200667
Wikidata QID: Q59112807
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description: scientific article; zbMATH DE number 6474205