Non commutative Khintchine and Paley inequalities
type: Item
instance of: scholarly article
title: Non commutative Khintchine and Paley inequalities
zbMATH Open document ID: 0755.47029
DOI: 10.1007/BF02384340
author: Françoise Lust-Piquard
author: Gilles Pisier
published in: Arkiv för Matematik
publication date: 1992-09-27T00:00:00Z
review text: Let \(E\) be a symmetric sequence space and let \(C_ E\) be the Schatten space of compact operators on a separable Hilbert space associated with \(E\). For the case \(E=\ell_ 1\) and for the more general case of 2- concave \(E\)'s a non-commutative analogue of Khinchin's inequality is proved. This analogue has been obtained as a consequence of the description of the space \(H^ 1_ \Lambda(C_ E)\), the range space of the projection \(P\otimes Id: H^ 1(C_ E)\to H^ 1(C_ E)\), where \(P: H^ 1(T)\to H^ 1_ \Lambda(T)\) (\(\Lambda=\{2^ n\mid\;n\geq 0\}\)) is the Paley projection. Boundedness of \(P\otimes Id: H^ 1(X)\to H^ 1(X)\) is also studied when \(X=Y\hat\otimes Z\) is the projective tensor product of Banach spaces satisfying some suitable assumptions.
reviewed by: Fedor Sukochev
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47A80
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 60551
zbMATH Keywords: Paley inequalities
zbMATH Keywords: symmetric sequence space
zbMATH Keywords: Schatten space of compact operators on a separable Hilbert space
zbMATH Keywords: non-commutative analogue of Khinchin's inequality
zbMATH Keywords: Paley projection
zbMATH Keywords: projective tensor product of Banach spaces
MaRDI profile type: Publication
cites work: Some remarks on interpolation theorems and the boundness or the triangular projection in unitary matrix spaces
cites work: Abstract Spectral Decompositions Guaranteed by the Hilbert Transform
cites work: Theorems of Hardy and Paley for Vector-Valued Analytic Functions and Related Classes of Banach Spaces
cites work: Some remarks on Banach spaces in which martingale difference sequences are unconditional
cites work: Q3737987
cites work: Q3234415
cites work: Q5618011
cites work: Solution of the similarity problem for cyclic representations of \(C^*- algebras\)
cites work: Factorization of Analytic Functions with Values in Non-Commutative L1-spaces and Applications
cites work: Q3687398
cites work: Q3997990
cites work: Q4188284
cites work: Q3721269
cites work: A Grothendieck factorization theorem on 2-convex Schatten spaces
cites work: On Fourier Multiplier Transformations of Banach-Valued Functions
cites work: Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
cites work: Q4765110
cites work: Notes on non-commutative integration
cites work: Grothendieck's theorem for noncommutative \(C^*\)-algebras, with an appendix on Grothendieck's constants
cites work: Q4169968
cites work: Q3715635
cites work: Q3744958
cites work: Factorization of operator valued analytic functions
cites work: Q4722940
cites work: Generalized Interpolation in H ∞
cites work: Q3857325
cites work: Q4768187
cites work: Uniform convexity of unitary ideals
cites work: Applications du théorème de factorisation pour des fonctions à valeurs opérateurs
full work available at URL: https://doi.org/10.1007/bf02384340
OpenAlex ID: W2056625421
description: scientific article; zbMATH DE number 60551