On operator algebras and operator ranges
type: Item
instance of: scholarly article
title: On operator algebras and operator ranges
zbMATH Open document ID: 0611.47035
DOI: 10.1007/BF01202518
author: P. Rosenthal
author: W. E. Longstaff
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: Some further results are given and some questions raised concerning operator algebras of countable range multiplicity. An example is given of an abelian range cyclic algebra that does not have finite strict multiplicity. On the other hand it is shown that every uniformly closed abelian range cyclic algebra is strictly cyclic. It is not known if the same conclusion holds for non-abelian algebras, even strongly closed ones. Additionally, it is shown that the commutant of a range cyclic algebra has a non-trivial invariant subspace. Nests of invariant subspaces of algebras of finite range multiplicity are also discussed.
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A15
zbMATH DE Number: 3988055
zbMATH Keywords: operator algebras of countable range multiplicity
zbMATH Keywords: abelian range cyclic algebra that does not have finite strict multiplicity
zbMATH Keywords: every uniformly closed abelian range cyclic algebra is strictly cyclic
zbMATH Keywords: commutant of a range cyclic algebra
zbMATH Keywords: invariant subspace
zbMATH Keywords: Nests of invariant subspaces of algebras of finite range multiplicity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3988055