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

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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 is similar to a -representation on .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0290118-0

Keywords:
Algebras of operators,
irreducible algebra,
irreducible representation,
-algebra

Article copyright:
© Copyright 1971
American Mathematical Society