Irreducible algebras of operators which contain a minimal idempotent.
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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Keywords: Algebras of operators, irreducible algebra, irreducible representation, -algebra
Article copyright: © Copyright 1971 American Mathematical Society