Irreducible algebras of operators which contain a minimal idempotent.
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- by Bruce A. Barnes
- Proc. Amer. Math. Soc. 30 (1971), 337-342
- DOI: https://doi.org/10.1090/S0002-9939-1971-0290118-0
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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 $\mathcal {H}$ is similar to a $^ \ast$-representation on $\mathcal {H}$.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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