Single-valued extension property at the points of the approximate point spectrum.
type: Item
instance of: scholarly article
title: Single-valued extension property at the points of the approximate point spectrum.
zbMATH Open document ID: 1036.47004
DOI: 10.1016/S0022-247X(02)00708-4
author: Pietro Aiena
author: E. Rosas
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: Let \(X\) be a complex Banach space. A linear bounded operator \(T\) on this space is said to have the single-valued extension property at the point \(\lambda_{0}\), if for every open disc \(D\) centered at \(\lambda_{0}\) the only analytic function \(f:D\rightarrow X\) which satisfies the equation \((\lambda I-T)f(\lambda)=0\) for all \(\lambda\in D\) is the function \(f\equiv 0\). The authors in the present paper obtain necessary and sufficient conditions for this property for operators from some special class. As a corollary of these results, they deduce several results on cluster points of some distinguished parts of the spectrum.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1915741
zbMATH Keywords: single-valued extension property
zbMATH Keywords: Fredholm theory
zbMATH Keywords: cluster points
zbMATH Keywords: spectrum
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00708-4
OpenAlex ID: W1999768947
description: scientific article; zbMATH DE number 1915741