A note on the commutants of CSL algebras modulo bimodules

De Guang Han
1992 Proceedings of the American Mathematical Society  
In this note, we show that for any cr-weakly closed bimodule M of a CSL algebra A satisfying M D A , the commutant of A modulo M is equal to M itself. Theorem 6 provided a result on the cohomology groups of CSL subalgebras of Von Neumann algebras. Throughout this paper, L(H) will be the set of all bounded linear operators on a complex Hubert space H. if Sf is a projection lattice in L(H) that is complete and 0, / e Sf, then we denote by algi? the set {Te L(H): Px TP = 0 for all P in J?}. algi?
more » ... ll P in J?}. algi? is said to be a CSL algebra if S? is commutative. By a bimodule M of a subalgebra A of L(H) in L(H), we mean a linear
doi:10.1090/s0002-9939-1992-1097342-1 fatcat:i3y2ipmsfjhc7c2g4jpllegukm