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Proceedings of the American Mathematical Society

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

 

 

A characterization of Hilbert modules


Author: George R. Giellis
Journal: Proc. Amer. Math. Soc. 36 (1972), 440-442
MSC: Primary 46K10
DOI: https://doi.org/10.1090/S0002-9939-1972-0320763-6
MathSciNet review: 0320763
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Abstract: For a proper $ {H^ \ast }$-algebra A, the relationship between $ ^ \ast $-representations of A and Hilbert modules is discussed. It is shown that a Hilbert module structure can be defined on every essential $ ^\ast$-representation of A.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0320763-6
Keywords: $ {H^ \ast }$-algebra, Hilbert module, vector inner product, $ ^ \ast $-representation
Article copyright: © Copyright 1972 American Mathematical Society