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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Nonselfadjoint representations of $ C^*$-algebras


Author: Heydar Radjavi
Journal: Proc. Amer. Math. Soc. 47 (1975), 133-136
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1975-0358367-4
MathSciNet review: 0358367
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Abstract: The following strengthening of a result of B. A. Barnes is proved: If $ \phi $ is a topologically irreducible representation of a $ {C^ \ast }$-algebra $ \mathfrak{A}$ on a Banach space such that $ \phi (\mathfrak{A})$ contains a nonzero finite-rank operator, then $ \phi $ is similar to an irreducible $ ^ \ast $-representation of $ \mathfrak{A}$(and is thus automatically continuous).


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DOI: https://doi.org/10.1090/S0002-9939-1975-0358367-4
Keywords: $ {C^ \ast }$-algebras, irreducible representations, transitive operator algebras on Banach spaces
Article copyright: © Copyright 1975 American Mathematical Society

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