Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Irreducible algebras of operators which contain a minimal idempotent.


Author: Bruce A. Barnes
Journal: Proc. Amer. Math. Soc. 30 (1971), 337-342
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9939-1971-0290118-0
MathSciNet review: 0290118
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that when A is a closed subalgebra of the bounded operators on a reflexive Banach space X, which acts irreducibly on X and contains a minimal idempotent, then every bounded operator with finite dimensional range on X is in A. We use this result to prove that every continuous irreducible representation of a GCR-algebra on a Hilbert space $ \mathcal{H}$ is similar to a $ ^ \ast $-representation on $ \mathcal{H}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.65

Retrieve articles in all journals with MSC: 46.65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0290118-0
Keywords: Algebras of operators, irreducible algebra, irreducible representation, $ {B^ \ast }$-algebra
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society