On Banach spaces \(Y\) for which \(B(C (\Omega), Y)= K(C (\Omega), Y)\)
type: Item
instance of: scholarly article
title: On Banach spaces \(Y\) for which \(B(C (\Omega), Y)= K(C (\Omega), Y)\)
zbMATH Open document ID: 0831.47015
author: Yanyan Li
published in: Pacific Journal of Mathematics
publication date: 1995-11-01T00:00:00Z
review text: Let \(\Omega\) be a compact Hausdorff space. In this paper, we give some necessary conditions and some sufficient conditions on a Banach space \(Y\) in order that all continuous operators from the space \(C(\Omega)\) into \(Y\) are compact. We prove that for a nonscattered compact Hausdorff space \(\Omega\) and for \(Y\) belonging to a large class of Banach spaces, all continuous operators from \(C(\Omega)\) into \(Y\) are compact if and only if all continuous operators from \(\ell^2\) into \(Y\) are compact.
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46A32
zbMATH DE Number: 811714
zbMATH Keywords: compact operators
zbMATH Keywords: scattered and nonscattered spaces
zbMATH Keywords: factorization of operators
zbMATH Keywords: nonscattered compact Hausdorff space
MaRDI profile type: Publication
full work available at URL: pjm.1995.169.201
OpenAlex ID: W1516464509
DOI: 10.2140/PJM.1995.169.201
description: scientific article; zbMATH DE number 811714