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)

 
 

 

The similarity problem for representations of $ C\sp{\ast} $-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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \pi :A \to B(H)$ be a bounded homomorphism of a $ {C^*}$-algebra into the bounded operators on a Hilbert space. We prove that, if $ \pi $ is cyclic, there is a $ *$-representation $ \theta :A \to B(H)$ and a bounded one-to-one positive operator $ P$ such that $ P\theta (a) = \pi (a)P$. We include applications to $ \theta $-derivations and invariant operator ranges for operator algebras.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05, 46L35

Retrieve articles in all journals with MSC: 46L05, 46L35


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

American Mathematical Society