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ISSN 1088-6826(e) ISSN 0002-9939(p)

Tensor products of $\sigma$ -weakly closed nest algebra submodules

Author(s): Dong Zhe
Journal: Proc. Amer. Math. Soc. 133 (2005), 1629-1637.
MSC (2000): Primary 47L75
Posted: December 21, 2004
MathSciNet review: 2120262
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Abstract: In this paper we prove that for any unital $\sigma$ -weakly closed algebra $\mathcal A$ which is $\sigma$ -weakly generated by finite-rank operators in $\mathcal A$ , every $\sigma$ -weakly closed $\mathcal A$ -submodule has $Property\; S_{\sigma}$ . In the case of nest algebras, if $\mathcal L_{1},\cdots,\mathcal L_{n}$ are nests, we obtain the following -fold tensor product formula:

$\begin{displaymath}\mathcal U_{\phi_{1}}{\overline{\otimes}}\cdots{\overline{\ot... ...{\phi_{n}}= \mathcal U_{\phi_{1}\otimes\cdots \otimes\phi_{n}},\end{displaymath}$

where each $\mathcal U_{\phi_{i}}$ is the $\sigma$ -weakly closed Alg $\mathcal L_{i}$ -submodule determined by an order homomorphism $\phi_{i}$ from $\mathcal L_{i}$ into itself.

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Additional Information:

Dong Zhe
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, 310027, People's Republic of China
Email: dongzhe@zju.edu.cn

DOI: 10.1090/S0002-9939-04-07838-4
PII: S 0002-9939(04)07838-4
Keywords: $Property\; S_{\sigma}$, tensor product, slice map
Received by editor(s): December 17, 2002
Posted: December 21, 2004
Additional Notes: This project was partially supported by the National Natural Science Foundation of China (No. 10401030) and the Zhejiang Nature Science Foundation (No. M103044)
Communicated by: David R. Larson
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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