Some classes of continuous operators on spaces of bounded vector-valued continuous functions with the strict topology
type: Item
instance of: scholarly article
title: Some classes of continuous operators on spaces of bounded vector-valued continuous functions with the strict topology
zbMATH Open document ID: 1343.46042
DOI: 10.1155/2015/796753
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 on \(X\), equipped with the strict topology \(\beta_\sigma\). We study the relationship between important classes of \((\beta_\sigma,\|\cdot\|_F)\)-continuous linear operators \(T: C_b(X,E)\to F\) (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived.
Mathematics Subject Classification ID: 46G10
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 6474239
zbMATH Keywords: strict topology
zbMATH Keywords: Riesz representing theorems
zbMATH Keywords: operators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/796753
OpenAlex ID: W2088188478
Wikidata QID: Q59112897
cites work: Q4519895
cites work: Bounded Continuous Functions on a Completely Regular Space
cites work: A survey of Baire measures and strict topologies
cites work: Strict Topologies for Vector-Valued Functions
cites work: Topologies on Spaces of Vector-Valued Continuous Functions
cites work: Convex compactness property in certain spaces of measures
cites work: Q4852573
cites work: Weak sequential convergence and weak compactness in spaces of vector-valued continuous functions
cites work: On Baire measures on D-topological spaces
cites work: Q4066057
cites work: Q4148368
cites work: Strongly bounded operators
cites work: Variational semi-regularity and norm convergence.
cites work: Operators on continuous function spaces and convergence in the spaces of operators
cites work: Weak precompactness, strong boundedness, and weak complete continuity
cites work: Strictly singular and strictly cosingular operators on spaces of continuous functions
cites work: Q5584192
cites work: Linear bounded transformation on the space of continuous functions
cites work: Some mapping properties of representing measures
cites work: Characterization of some classes of operators on spaces of vector-valued continuous functions
cites work: Q3743905
cites work: On Weakly Compact Operators on Spaces of Vector Valued Continuous Functions
cites work: Strictly Singular and Strictly Cosingular Operators on C(K, E)
cites work: Some classes of operators on \(C(K,E)\). Extensions and applications
cites work: Linear Operators and Vector Measures
cites work: On representation of linear operators on $C_0(T,{\bf X})$
cites work: Weakly compact, unconditionally converging, and Dunford-Pettis operators on spaces of vector-valued continuous functions
cites work: On unconditionally converging and weakly precompact operators
cites work: Nuclear operators on spaces of continuous vector-valued functions
cites work: Spaces on which unconditionally converging operators are weakly completely continuous
cites work: Q5660183
cites work: Spaces of Vector Measures
cites work: Compactness in spaces of measures
cites work: Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)
cites work: Q3329946
cites work: On integration in Banach spaces, I
cites work: Operators on the space of bounded strongly measurable functions
cites work: Banach spaces of vector-valued functions
cites work: An averaging result for \(l^ 1-\)sequences and applications to weakly conditionally compact sets in \(L^ 1\).
cites work: Q3683058
cites work: On bases and unconditional convergence of series in Banach spaces
cites work: Q5573683
cites work: Q5613420
cites work: The comparison of an unconditionally converging operator
description: scientific article; zbMATH DE number 6474239