Search results for "Bicommutant"
showing 3 items of 3 documents
Partial O*-Algebras
2002
This chapter is devoted to the investigation of partial O*-algebras of closable linear operators defined on a common dense domain in a Hilbert space. Section 2.1 introduces of O- and O*-families, O- and O*-vector spaces, partial O*-algebras and O*-algebras. Partial O*-algebras and strong partial O*-algebras are defined by the weak and the strong multiplication. Section 2.2 describes four canonical extensions (closure, full-closure, adjoint, biadjoint) of O*-families and defines the notions of closedness and full-closedness (self-adjointness, integrability) of O*-families in analogy with that of closed (self-adjoint) operators. Section 2.3 deals with two weak bounded commutants M′w and M′qw …
MR2851064 Daws, Matthew A bicommutant theorem for dual Banach algebras. Math. Proc. R. Ir. Acad. 111A (2011), no. 1, 21–28. (Reviewer: Camillo Trapan…
2012
Bicommutants of reduced unbounded operator algebras
2009
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.