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- W2964269964 abstract "We introduce the notion of a regular mapping on a non-commutative L p -space associated to a hyperfinite von Neumann algebra for 1 ≤ p ≤ ∞. This is a non-commutative generalization of the notion of regular or order bounded map on a Banach lattice. This extension is based on our recent paper [P3], where we introduce and study a non-commutative version of vector valued L p -spaces. In the extreme cases p = 1 and p = ∞, our regular operators reduce to the completely bounded ones and the regular norm coincides with the cb-norm. We prove that a mappings is regular iff it is a linear combination of bounded, completely positive mappings. We prove an extension theorem for regular mappings defined on a subspace of a non-commutative L p -space. Finally, let R p be the space of all regular mappings on a given non-commutative L p -space equipped with the regular norm. We prove the isometric identity R p = (R∞, R 1 ) θ where θ = 1/p and where (., .) θ is the dual variant of Calderon's complex interpolation method" @default.
- W2964269964 created "2019-07-30" @default.
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- W2964269964 date "1993-08-01" @default.
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- W2964269964 title "Regular operators between non-commutative $L_p$-spaces" @default.
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