On the largest analytic set for cyclic operators
type: Item
instance of: scholarly article
title: On the largest analytic set for cyclic operators
zbMATH Open document ID: 1054.47005
DOI: 10.1155/S0161171203209042
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/51128
review text: The author gives a complete discription of the largest analytic set for cyclic Hilbert-space operators and explains more about bounded point evaluations from the point of view of local spectral theory. Also, the author proves for every cyclic Banach-space operator \(T\in B(X)\) possessing Bishop's property \((\beta)\), that the set \(\sigma(T)\setminus \sigma_{ap}(T)\) is the open set of complex numbers \(\lambda\in\mathbb{C}\) for which there exists a nonzero analytic function \(\varphi:V\to X^*\) on some open disc \(V\) centered at \(\lambda\) satisfying \((T^*- \alpha)\phi(\alpha)= 0\) for all \(\alpha\) in \(V\). By this result, it is shown that densely similar cyclic Banach-space operators possessing Bishop's property \((\beta)\) have the same approximate point spectra, which generalizes Theorem 4 of the article by \textit{M. Raphael} [Indiana Univ. Math. J. 31, 243--246 (1982; Zbl 0455.47020)].
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 47B20
zbMATH DE Number: 2012526
zbMATH Keywords: single-valued extension property
zbMATH Keywords: analytic bounded point evaluation
zbMATH Keywords: Bishop's property
zbMATH Keywords: cyclic Banach-space operator
author: Abdellatif Bourhim
reviewed by: Bahmann Yousefi
MaRDI profile type: Publication
OpenAlex ID: W2096949948
description: scientific article; zbMATH DE number 2012526