Introduction to Operator Space Theory

By G. Pisier. 2003

812 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f43e8d76670f657c1db0a5b50f760f5c5f34d536

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In Mathematical Physics

Citations in the corpus

Khintchine type inequalities for reduced free products and applications (2005, background): “This allows to show that the subspace generated by the words of length d in a reduced free product is complemented with a constant depending linearly on d.”
ABOUT THE QWEP CONJECTURE (2003, methodology): “We refer the reader to the books of Effros and Ruan [ER2] and of Pisier [ Pi2 ].”
The tetrablock as a spectral set (2014, background): “er and Young [5] - [7]. (3) No subset of C3 with property P is known. (4) If K is the closed unit ball of some norm on Cn where n > 2, then K cannot have this property. See Paulsen [21] and Pisier [23]. Theorem 1.2.2 and the remark following it in Arveson [10] gives a novel idea that has been tak”
Smooth Fourier multipliers on group von Neumann algebras (2010, methodology): “Two excellent books on operator space theory are Effros/Ruan and Pisier monographs [12, 64].”
Matrix concentration inequalities and free probability (2021, background): “In contrast, many problems in areas such as functional analysis [15, 31] and in applied mathematics [5, 39] fall outside the scope of classical random matrix theory.”
Structured Random Matrices (2016, background): “ 2p −1 "Xs k=1 A2 k #1/2 when n = 1. It was realized by Lust-Piquard [13] that the analogous inequality holds in any dimension n (the correct dependence of the bound on p was obtained later, cf. [17]). Theorem 3.2 (Noncommutative Khintchine inequality). In the present setting E[Tr[X2p]]1/2p ≤ p”
Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory (2007, positive): “In the language of operator space theory and following Pisier’s characterization [45, 46] of complete boundedness we immediately obtain: Corollary.”
Characterisations of the weak expectation property (2013, background): “There are alternate proofs for the assertion that C(Fn) has LP: see [23, 28], for example.”