On the Tensor Products of Maximal Abelian JW-Algebras
It is well known in the work of Kadison and Ringrose (1983)that if 𝐴 and 𝐵 are maximal abelian von Neumann subalgebras of von Neumann algebras 𝑀 and 𝑁, respectively, then 𝐴⊗𝐵 is a maximal abelian von Neumann subalgebra of 𝑀⊗𝑁. It is then natural to ask whether a similar result holds in the context o...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/621386 |
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| Summary: | It is well known in the work of Kadison and Ringrose (1983)that if 𝐴 and 𝐵 are maximal abelian von Neumann subalgebras of von Neumann algebras 𝑀 and 𝑁, respectively, then 𝐴⊗𝐵 is a maximal abelian von Neumann subalgebra of 𝑀⊗𝑁. It is then natural to ask whether a similar result holds in the context of
𝐽𝑊-algebras and the 𝐽𝑊-tensor product. Guided to some extent by the close
relationship between a 𝐽𝑊-algebra M and its universal enveloping von Neumann algebra 𝑊∗(𝑀), we seek in this article to investigate the answer to this question. |
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| ISSN: | 0161-1712 1687-0425 |