Abstract :
For an operator bimodule X over von Neumann algebras A ⊆ B(H) and B ⊆ B(K), the
space of all completely bounded A,B-bimodule maps from X into B(K,H), 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 Xn is associated so
that completely bounded A,B-bimodule maps from X into normal operator bimodules factorize
uniquely through Xn. A construction of Xn 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.
