2003/07/31 by B. Magajna
Mathematics · #math.OA #math.FA #msc:46L07 #msc:46H25 #msc:47L25
published as J.F.A. 219/2, pp. 306--339, February 2005 · The first version of the paper has been split into two parts, corrected and a few results added. This is the first part
arxiv created 2004/12/07 · arxiv updated 2009/12/01
For an operator bimodule X over von Neumann algebras A⊆\bh and B⊆\bk, the space of all completely bounded A,B-bimodule maps from X into \bkh, 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 \norX is associated so that completely bounded A,B-bimodule maps from X into normal operator bimodules factorize uniquely through \norX. A construction of \norX 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.