The Grothendieck inequality for bilinear forms on C∗-algebras
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TLDR
For any bounded bilinear form V on a pair of C∗-algebras A, B, there exist two states ϕ1, ϕ2 on A and ψ 1, ψ 2 on B, such that |V(x,y)|⩽‖V|(ϕ 1 (x ∗ x)+ϕ 2 (xx 2 )) 1 2 (φ 1 (y ∗ y)+About:
This article is published in Advances in Mathematics.The article was published on 1985-05-01 and is currently open access. It has received 167 citations till now. The article focuses on the topics: Grothendieck inequality & Bilinear form.read more
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Grothendieck's Theorem, past and present
TL;DR: The Grothendieck constant of a graph has been introduced in graph theory and in computer science as discussed by the authors, where it is invoked to replace certain NP hard problems by others that can be treated by semidefinite programming and hence solved in polynomial time.
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Symmetric amenability and the nonexistence of Lie and Jordan derivations
TL;DR: The theory of amenable Banach algebras has been studied in this article, where it is shown that if a Banach algebra has an approximate diagonal consisting of symmetric tensors, then every continuous Jordan derivation into an -bimodule is a derivation.
Natural norms on symmetric tensor products of normed spaces
TL;DR: The basics of the theory of symmetric tensor products of normed spaces and some applications are presented in this paper, where some applications of the tensor product theory are discussed.
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Grothendieck’s theorem for operator spaces
TL;DR: In this paper, it was shown that if E, F are C *-algebras, of which at least one is exact, then every completely bounded T:E→F * can be factorized through the direct sum of the row and column Hilbert operator spaces.
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Ultraproducts in Banach space theory.
TL;DR: The first step into Banach space theory was prepared by the development of the local theory of Banach spaces which goes back to the work of J. Lindenstrauss, A. P. Rosenthal and R. C. James as mentioned in this paper.
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Grothendieck's theorem for noncommutative C∗-algebras, with an Appendix on Grothendieck's constants
TL;DR: In this paper, a conjecture of Grothendieck on bilinear forms on a C∗-algebra Ol is studied, and it is shown that every approximateable operator from Ol into Ol ∗ factors through a Hilbert space.
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Solution of the similarity problem for cyclic representations of C*-algebras
TL;DR: In this paper, the authors considered the problem of finding a non-selfadjoint representation of a C*-algebra A on a Hilbert space similar to a unitary representation.