Backward shifts on Banach spaces \(C(X)\)
type: Item
instance of: scholarly article
title: Backward shifts on Banach spaces \(C(X)\)
zbMATH Open document ID: 0878.47014
author: M. Rajagopalan
author: K. Sundaresan
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-09-30T00:00:00Z
review text: A backward shift on a Banach space \(E\) is an operator \(T\) with one-dimensional kernel such that the corresponding operator from the quotient of \(E\) by the kernel of \(T\) is an isometry and so that \(\bigcup_{n\geq 1}\text{Ker }T^n\) is dense in \(E\). The authors settle a conjecture of J. R. Holub (in a stronger form) by proving that for no infinite compact space \(X\) is there a backward shift on \(C(X)\).
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 930204
zbMATH Keywords: backward shift
zbMATH Keywords: one-dimensional kernel
reviewed by: James B. Cooper
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0329
OpenAlex ID: W2062614406
DOI: 10.1006/JMAA.1996.0329
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description: scientific article; zbMATH DE number 930204