The similarity problem for representations of -algebras

Author:
John W. Bunce

Journal:
Proc. Amer. Math. Soc. **81** (1981), 409-414

MSC:
Primary 46L05; Secondary 46L35

DOI:
https://doi.org/10.1090/S0002-9939-1981-0597652-0

MathSciNet review:
597652

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded homomorphism of a -algebra into the bounded operators on a Hilbert space. We prove that, if is cyclic, there is a -representation and a bounded one-to-one positive operator such that . We include applications to -derivations and invariant operator ranges for operator algebras.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0597652-0

Keywords:
The similarity problem,
derivations,
invariant operator range,
Pisier's inequality

Article copyright:
© Copyright 1981
American Mathematical Society