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Proceedings of the American Mathematical Society

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

 
 

 

On biduals of $ C\sp *$-tensor products


Author: John C. Quigg
Journal: Proc. Amer. Math. Soc. 100 (1987), 666-668
MSC: Primary 46L05; Secondary 46M05
DOI: https://doi.org/10.1090/S0002-9939-1987-0894435-4
MathSciNet review: 894435
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Abstract: Huruya [4] has proven that, for $ {C^*}$-algebras $ {A_1}$ and $ {A_2}$,

$\displaystyle {({A_1} \otimes {A_2})^{**}} = A_1^{**}\overline \otimes A_2^{**}$

for every $ {A_2}$ if and only if $ {A_1}$ is scattered. We strengthen this by proving that $ {({A_1} \otimes {A_2})^{**}} = A_1^{**}\overline \otimes A_2^{**}$ if and only if $ {A_1}$ or $ {A_2}$ is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of $ {W^*}$-tensor products.

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DOI: https://doi.org/10.1090/S0002-9939-1987-0894435-4
Article copyright: © Copyright 1987 American Mathematical Society

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