Duality and asymptotic spectral decompositions
type: Item
instance of: scholarly article
title: Duality and asymptotic spectral decompositions
zbMATH Open document ID: 0613.47029
author: Ridgley Lange
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Decomposable operators in the sense of C. Foiaş are operators in a Banach space, for which a reasonably rich supply of invariant subspaces with reasonable spectral localization properties exist. A variety of this notion has been considered in the literature, and the introduction of this paper gives a good review of the main classes of these operators: e.g. strongly, weakly, analytically decomposable operators, and operators having an asymptotic spectral decomposition (ASD). In the paper several other similar classes are also considered, e.g. quasi-decomposable, strongly quasi-decomposable, strongly bi-decomposable and boundedly decomposable operators. 11 theorems are proved on the connections among these classes, using in many cases the duality theory, and assuming in several cases that the underlying space is reflexive. A sample (Theorem 8): Let the space be reflexive. If the operator T has an (ASD) such that each invariant subspace can be chosen strongly analytic, then T is decomposable.
Mathematics Subject Classification ID: 47B40
zbMATH DE Number: 3992238
zbMATH Keywords: invariant subspaces
zbMATH Keywords: spectral localization properties
zbMATH Keywords: strongly, weakly, analytically decomposable operators
zbMATH Keywords: operators having an asymptotic spectral decomposition
zbMATH Keywords: strongly quasi-decomposable
zbMATH Keywords: strongly bi- decomposable
zbMATH Keywords: boundedly decomposable operators
zbMATH Keywords: duality theory
zbMATH Keywords: reflexive
MaRDI profile type: Publication
full work available at URL: pjm.1986.121.93
OpenAlex ID: W2055374552
DOI: 10.2140/PJM.1986.121.93
description: scientific article; zbMATH DE number 3992238