A commutant of an unbounded operator algebra

Inoue, Atsushi

doi:10.1090/S0002-9939-1978-0473863-X

A commutant of an unbounded operator algebra
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Proc. Amer. Math. Soc. 69 (1978), 97-102 Request permission

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 $E{W^\# }$-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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Les algèbres d’opérateurs dans l’espace hilbertien

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