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Proceedings of the American Mathematical Society

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

 

 

Trace-class for a Hilbert module


Author: George R. Giellis
Journal: Proc. Amer. Math. Soc. 29 (1971), 63-68
MSC: Primary 46.65; Secondary 47.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0276783-2
MathSciNet review: 0276783
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Abstract: Let H be a Hilbert module over a proper $ {H^ \ast }$-algebra A, and let $ \tau (H) = \{ fa:f \in H,a \in A\} $. Then we define a Banach space norm on $ \tau (H)$ so that the module operation is continuous with respect to both variables. $ \tau (H)$ is shown to be the dual of a certain space of bounded operators from H to A, and the dual of $ \tau (H)$ is also identified.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276783-2
Keywords: $ {H^ \ast }$-algebra, orthogonal projection base, trace norm, centralizer, Hilbert module, vector inner product
Article copyright: © Copyright 1971 American Mathematical Society