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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An irreducible representation of a symmetric star algebra is bounded


Author: Subhash J. Bhatt
Journal: Trans. Amer. Math. Soc. 292 (1985), 645-652
MSC: Primary 46K10; Secondary 47D40
MathSciNet review: 808743
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Abstract: A $ {\ast}$-algebra $ A$ is called symmetric if $ (1 + {x^{\ast}}x)$ is invertible in $ A$ for each $ x$ in $ A$. An irreducible hermitian representation of a symmetric $ {\ast}$-algebra $ A$ maps $ A$ onto an algebra of bounded operators.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0808743-9
PII: S 0002-9947(1985)0808743-9
Keywords: Symmetric $ {\ast}$-algebra, unbounded representations
Article copyright: © Copyright 1985 American Mathematical Society