Duality and normal parts of operator modules

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• 作者：Magajna ; Bojan
• 关键词：primary 46L07 ; 46H25 ; secondary 47L25 ; Operator bimodule ; von Neumann algebra ; Relative tensor products
• 刊名：Journal of Functional Analysis
• 出版年：2005
• 出版时间：February 15, 2005
• 年：2005
• 卷：219
• 期：2
• 页码：306-339
• 全文大小：430 K

文摘

For an operator bimodule X over von Neumann algebras Formula Not Shown and Formula Not Shown, the space of all completely bounded Formula Not Shown -bimodule maps from X into Formula Not Shown, 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 Formula Not Shown is associated so that completely bounded Formula Not Shown -bimodule maps from X into normal operator bimodules factorize uniquely through Formula Not Shown . A construction of Formula Not Shown 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.