Growth conditions, compact perturbations and operator subdecomposability, with applications to generalized Cesàro operators
type: Item
instance of: scholarly article
title: Growth conditions, compact perturbations and operator subdecomposability, with applications to generalized Cesàro operators
zbMATH Open document ID: 1061.47031
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-01-26T00:00:00Z
review text: Let \(X\) be a complex Banach space and let \(L(X)\) denote the space of bounded operators on \(X\). An operator \(T \in L(X)\) is said to have Bishop's property \((\beta)\) if, whenever \((f_{n})_{n}\) is a sequence of analytic \(X\)-valued functions such that \((\lambda - T)f_{n}(\lambda) \rightarrow 0\) uniformly on the compact subsets of an open subset \(U\) of the complex plane, then \(f_{n}(\lambda) \rightarrow 0\) uniformly on the compact subsets of \(U\). Among other results, the authors show that for several classes of analytic symbols \(\phi\), the corresponding generalized Cesàro operator \(S_{\phi}\) acting on the Hardy space \(H^{p}, 1 < p < \infty\), has Bishop's property \((\beta)\) and admits a decomposable extension.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 47B40
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 2131157
zbMATH Keywords: Bishop's property(\(\beta\))
zbMATH Keywords: decomposable operator
zbMATH Keywords: Hardy space
zbMATH Keywords: Cesàro operator
author: T. L. Miller
author: V. G. Miller
author: Michael M. Neumann
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.07.007
OpenAlex ID: W2023119343
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DOI: 10.1016/J.JMAA.2004.07.007
description: scientific article; zbMATH DE number 2131157