Representations of \(H^ \infty(G)\) and invariant subspaces
type: Item
instance of: scholarly article
title: Representations of \(H^ \infty(G)\) and invariant subspaces
zbMATH Open document ID: 0813.47009
DOI: 10.1007/BF01459732
author: Jörg Eschmeier
published in: Mathematische Annalen
publication date: 1995-05-28T00:00:00Z
full work available at URL: https://eudml.org/doc/165168
review text: The author considers the algebra of bounded, complex functions, analytic on \(G\), a bounded, open subset of the complex plane. Representations of this algebra in the algebra of linear, bounded operators acting on a Banach space are considered. The Banach space is supposed to satisfy certain geometrical conditions. In all cases these conditions hold for reflexive Banach spaces. The author proves that if the image under this representation of the identity function \(z\), is an operator with spectrum dominating for \(G\), then, under some supplementary conditions, the image of the algebra of bounded, analytic functions under the given representation is shown to have a rich invariant subspace lattice. Among other things, the author proves this last operator algebra is reflexive.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 537314
zbMATH Keywords: representations
zbMATH Keywords: operator algebra
zbMATH Keywords: reflexive
reviewed by: V. Matache
MaRDI profile type: Publication
cites work: Q4743324
cites work: The algebra of multiplication operators on Bergman spaces
cites work: A note on disjoint invariant subspaces
cites work: Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II
cites work: Invariant subspaces, dilation theory, and the structure of the predual of a dual algebra. I
cites work: Two Banach space methods and dual operator algebras
cites work: (BCP)-operators are reflexive
cites work: Q5678038
cites work: Q3039954
cites work: Q3329946
cites work: Q3479060
cites work: Invariant subspaces for operators with Bishop's property \((\beta{})\) and thick spectrum
cites work: Q3941912
cites work: Reflexivity of N-tuples of contractions with rich joint left essential spectrum
cites work: BANACH Coherent Analytic FRÉCHET Sheaves
cites work: Algebras of subnormal operators
cites work: Q3732367
cites work: The space of bounded analytic functions on a region
cites work: Q3920145
cites work: The analytic-functional calculus for several commuting operators
cites work: Q3958979
cites work: On \(C_{00}\)-contractions with dominating spectrum
cites work: Q3200088
description: scientific article; zbMATH DE number 537314