Components of generalized Kato resolvent set and single-valued extension property
type: Item
instance of: scholarly article
title: Components of generalized Kato resolvent set and single-valued extension property
zbMATH Open document ID: 1287.47002
author: Qiaofen Jiang
author: Huaijie Zhong
published in: Frontiers of Mathematics in China
publication date: 2012-11-07T00:00:00Z
review text: The authors study the components of the generalized Kato resolvent set. From the constancy of some subspace valued mappings on the components of the generalized Kato resolvent set [\textit{W. Bouamama}, Rend. Circ. Mat. Palermo (2) 53, No.~3, 313--324 (2004; Zbl 1195.47011)] and, in the case of operators which admit a generalized Kato decomposition, the equivalences of the single-valued extension property at a point, the authors obtain a classification of these components, which extends the results of \textit{P. Aiena} and \textit{F. Villafañe} [Contemp. Math. 328, 1--14 (2003; Zbl 1057.47006)] to the components of the generalized Kato resolvent set. The authors also present some applications of their results.
reviewed by: Yufeng Lu
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 47A53
zbMATH DE Number: 6103003
zbMATH Keywords: Banach space
zbMATH Keywords: generalized Kato decomposition
zbMATH Keywords: single-valued extension property
MaRDI profile type: Publication
full work available at URL: s11464-012-0207-4
OpenAlex ID: W1516526721
cites work: Q3154380
cites work: Operators which have a closed quasi-nilpotent part
cites work: On a Localised Single–Valued Extension Property
cites work: Operators which do not have the single valued extension property
cites work: Q4415357
cites work: Single-valued extension property at the points of the approximate point spectrum.
cites work: Q4462300
cites work: Pseudo-Fredholm operators in Banach spaces
cites work: Spectral theory. II. Resolutions of the identity
cites work: Spectral operators
cites work: Q5654646
cites work: The single valued extension property on a Banach space
cites work: The Unconditional Basic Sequence Problem
cites work: Generalized Kato decomposition, single-valued extension property and approximate point spectrum
cites work: A generalized Drazin inverse
cites work: Isolated spectral points
cites work: Generalisation de la decomposition de kato aux opérateurs paranormaux et spectraux
cites work: Q4713702
cites work: Sur la Theorie Spectrale Locale et Limite des Nilpotents
cites work: SEMI-FREDHOLM OPERATORS AND LOCAL SPECTRAL THEORY
cites work: Continuity of the generalized kernel and range of semi-Fredholm operators
DOI: 10.1007/S11464-012-0207-4
description: scientific article; zbMATH DE number 6103003