The unbounded bicommutant M_E’ of the reduction of an O*-algebraM via a given projection E' weakly commuting with 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.
Bagarello, F., Inoue, A., Trapani, C. (2009). Bicommutants of reduced unbounded operator algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009 [10.1090/S0002-9939-09-10023-0].
Bicommutants of reduced unbounded operator algebras
BAGARELLO, Fabio;TRAPANI, Camillo
2009-01-01
Abstract
The unbounded bicommutant M_E’ of the reduction of an O*-algebraM via a given projection E' weakly commuting with 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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