A Remark about the Connes Fusion Tensor Product
نویسنده
چکیده
We analyze the algebraic structure of the Connes fusion tensor product (CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra M . It turns out that all complications in its definition disappear if one uses the closely related bi-modules of bounded vectors. We construct an equivalence of monoidal categories with duality between a category of Hilbert bi-modules over M with CFTP and some natural category of bi-modules over M with the usual relative algebraic tensor product.
منابع مشابه
Bessel multipliers on the tensor product of Hilbert $C^ast-$ modules
In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...
متن کاملThe relative tensor product and a minimal fiber product in the setting of C-algebras
We introduce a relative tensor product of C∗-modules and a spatial fiber product of C∗-algebras that are analogues of Connes’ fusion of correspondences and the fiber product of von Neumann algebras introduced by Sauvageot, respectively, and study their categorical properties. These constructions form the basis for our approach to quantum groupoids in the setting of C∗-algebras that is published...
متن کاملA remark on asymptotic enumeration of highest weights in tensor powers of a representation
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...
متن کاملBEST APPROXIMATION IN QUASI TENSOR PRODUCT SPACE AND DIRECT SUM OF LATTICE NORMED SPACES
We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...
متن کاملConnes ’ embedding problem and Tsirelson ’ s problem
We show that Tsirelson’s problem concerning the set of quantum correlations and Connes’ embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg’s QWEP conjecture) are essentially equivalent. Specifically, Tsirelson’s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the...
متن کامل