Duality and normal parts of operator modules |
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Authors: | Bojan Magajna |
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Affiliation: | Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia |
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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. |
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Keywords: | primary 46L07 46H25 secondary 47L25 |
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