A Remark on W*-Tensor Products of W*-Algebras

Corneliu Constantinescu ()

Chapter Chapter 4 in Nonlinear Analysis and Variational Problems, 2010, pp 37-52 from Springer

Abstract: Abstract Let E be a W*-algebra, T a hyperstonian compact space, C(T) the W*-algebra of continuous scalar valued functions on T, and F(T,E) the set of bounded maps x : T → E such that for every element a of the predual of E the function $$T \to {\rm{IK,}}\,\,\,\,\,\,\,\,\,t \mapsto \langle x_t ,a\rangle $$ is continuous. We define for every x ∈ F(T,E) an element $$\tilde x$$ ∈ C(T) $$\bar \otimes $$ E such that the map $$f(T,E) \to b(T)\bar \otimes E,\,\,\,\,\,\,\,x \mapsto \tilde x$$ is a bijective isometry of ordered involutive Banach spaces (where this structure on F(T,E) is defined pointwise). In general F(T,E) is not an algebra for the pointwise multiplication, but for x,y,z ∈ F(T,E) we characterize the case when $$\tilde x\tilde y = \tilde z$$ .

Keywords: Hilbert Space; Tensor Product; Orthogonal Projection; Pairwise Disjoint; Dual Norm (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4419-0158-3_4

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