Duality and Normal Parts of Operator Modules

الأصل · EN

For an operator bimodule X over von Neumann algebras A and B, the space of all completely bounded A,B-bimodule maps from X into, is the bimodule dual of X. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To X a normal operator bimodule X is associated so that completely bounded A,B-bimodule maps from X into normal operator bimodules factorize uniquely through X. A construction of X in terms of biduals of X, A and B is presented. Various operator bimodule structures are considered on a Banach bimodule admitting a normal such structure.