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Proceedings of the American Mathematical Society

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

 

 

A commutant of an unbounded operator algebra


Author: Atsushi Inoue
Journal: Proc. Amer. Math. Soc. 69 (1978), 97-102
MSC: Primary 46L15
DOI: https://doi.org/10.1090/S0002-9939-1978-0473863-X
MathSciNet review: 0473863
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Abstract: A commutant $ {\mathfrak{A}^c}$ and bicommutant $ {\mathfrak{A}^{cc}}$ of an unbounded operator algebra $ \mathfrak{A}$ called a #-algebra are defined. The first purpose of this paper is to investigate whether the bicommutant $ {\mathfrak{A}^{cc}}$ of a #-algebra $ \mathfrak{A}$ is an $ E{W^\char93 }$-algebra, as defined in [6], or not. The second purpose is to investigate the relation between $ {\mathfrak{A}^{cc}}$ and topologies on a #-algebra $ \mathfrak{A}$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0473863-X
Article copyright: © Copyright 1978 American Mathematical Society