Proceedings of the American Mathematical Society

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

Bicommutants of reduced unbounded operator algebras

Author(s): Fabio Bagarello; Atsushi Inoue; Camillo Trapani
Journal: Proc. Amer. Math. Soc. 137 (2009), 3709-3716.
MSC (2000): Primary 47L60
Posted: June 29, 2009
MathSciNet review: 2529878
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Abstract | References | Similar articles | Additional information

Abstract: The unbounded bicommutant $(\mathfrak{M}_{E'})''_{\mathrm{wc}}$ of the reduction of an O*-algebra $\mathfrak{M}$ via a given projection weakly commuting with $\mathfrak{M}$ is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.

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