Tensor products of operator spaces
David P. Blecher,Vern I. Paulsen +1 more
TLDR
In this article, the authors lay the foundations for a systematic study of tensor products of subspaces of C∗-algebras and employ various notions of duality.About:
This article is published in Journal of Functional Analysis.The article was published on 1991-08-01 and is currently open access. It has received 311 citations till now. The article focuses on the topics: Dual norm & Operator norm.read more
Citations
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Journal Article
Non-commutative vector valued Lp-spaces and completely p-summing maps
TL;DR: The notion of completely p-summing maps was introduced in this paper, which is the operator space analogue of the $p$-absolutely summing maps in the sense of Pietsch-Kwapie\'n.
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Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces
Marek Bożejko,Roland Speicher +1 more
TL;DR: In this paper, it was shown that quasi-multiplicative mappings on permutation groups, determined by self-adjoint contractions fulfilling the braid or Yang-Baxter relations, are completely positive.
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Approximation properties for group *-algebras and group von Neumann algebras
Uffe Haagerup,Jon Kraus +1 more
TL;DR: In this article, it was shown that the class of groups with the approximation property (AP) is stable with respect to semidirect products, and more generally this class is stable for group extensions.
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The standard dual of an operator space.
TL;DR: The notion of projectivity for operator spaces has been introduced independently by Paulsen and Ruan as discussed by the authors, and its significance in the theory of tensor products has already been partially explored by the aforementioned.
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Extensions of locally compact quantum groups and the bicrossed product construction
Stefaan Vaes,Leonid Vainerman +1 more
TL;DR: In this paper, the authors develop the cocycle bicrossed product construction, starting from a matched pair of locally compact quantum groups, and define exact sequences and establish a one-to-one correspondence between cocyclic products and cleft extensions.
References
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MonographDOI
Factorization of Linear Operators and Geometry of Banach Spaces
TL;DR: In this paper, the authors present operators and basic applications for factorization through a Hilbert space Type and cotype, and apply them to Grothendieck's conjecture and the volume ratio method.
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Injectivity and operator spaces
Man-Duen Choi,Edward G. Effros +1 more
TL;DR: Injective von Neumann algebras R are characterized by any one of the following: (1) a relative interpolation property, (2) a finite "projectivity" property, and (3) an approximate factorization as discussed by the authors.