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Proceedings of the American Mathematical Society

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

 
 

 

$\sigma$-weakly closed modules of certain reflexive operator algebras


Author: Pei Xin Chen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1751-1756
MSC: Primary 47D25; Secondary 46H25, 47B47
DOI: https://doi.org/10.1090/S0002-9939-1995-1246534-X
MathSciNet review: 1246534
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Abstract: Let $\mathcal {A}$ be a completely distributive CSL algebra and let M be any $\sigma$-weakly closed $\mathcal {A}$-module. We give characterizations of commutant $C(\mathcal {A},M)$ of $\mathcal {A}$ modulo M and AlgLat M. Furthermore, we deal with the relations among $\mathcal {A},C(\mathcal {A},M)$ and AlgLat M.


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Keywords: <!– MATH $\mathcal {A}$ –> <IMG WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\mathcal {A}$">-module, reflexive operator algebra, commutant of <!– MATH $\mathcal {A}$ –> <IMG WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\mathcal {A}$"> modulo module
Article copyright: © Copyright 1995 American Mathematical Society