Tensor products of preclosed operators on 𝐶*-algebras

Wu, Liang Sen

doi:10.1090/S0002-9939-1983-0695256-4

Tensor products of preclosed operators on $C^{\ast }$-algebras
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by Liang Sen Wu

Proc. Amer. Math. Soc. 88 (1983), 265-269

DOI: https://doi.org/10.1090/S0002-9939-1983-0695256-4

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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 $|| \cdot |{|_{\min }}$ is reflexive on the algebraic tensor product ${A_1} \otimes {A_2}$.

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