Bicommutants of reduced unbounded operator algebras

Details Bicommutants of reduced unbounded operator algebras Bicommutants of reduced unbounded operator algebras

2009-04-06

arxiv.org/abs/0904.0881v1

Physics

Mathematical Physics

Proc. of the Amer. Math. Soc., in press

Scientific paper

The unbounded bicommutant $(\mathfrak M_{E'})''$ of the {\em reduction} of an
O*-algebra $\MM$ via a given projection $E'$ 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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