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Proceedings of the American Mathematical Society

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

 

 

Tensor products of preclosed operators on $ C\sp{\ast} $-algebras


Author: Liang Sen Wu
Journal: Proc. Amer. Math. Soc. 88 (1983), 265-269
MSC: Primary 46L05; Secondary 46M05, 47C15
MathSciNet review: 695256
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Abstract: In this paper, we prove the following result: If $ {A_1}$, $ {A_2}$ are $ {C^ * }$-algebras, and $ {T_1}$, $ {T_2}$ are preclosed operators on $ {A_1}$, $ {A_2}$ respectively, then $ {T_1} \otimes {T_2}$ is preclosed on $ {A_1}{ \otimes _{\min }}{A_2}$. Furthermore, we show that the injective $ {C^ * }$-cross norm $ \vert\vert \cdot \vert{\vert _{\min }}$ is reflexive on the algebraic tensor product $ {A_1} \otimes {A_2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0695256-4
Article copyright: © Copyright 1983 American Mathematical Society