On the best constants in noncommutative Khintchine-type inequalities |
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Authors: | Uffe Haagerup Magdalena Musat |
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Institution: | aDepartment of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark;bDepartment of Mathematical Sciences, University of Memphis, 373 Dunn Hall, Memphis, TN 38152, USA |
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Abstract: | We obtain new proofs with improved constants of the Khintchine-type inequality with matrix coefficients in two cases. The first case is the Pisier and Lust-Piquard noncommutative Khintchine inequality for p=1, where we obtain the sharp lower bound of in the complex Gaussian case and for the sequence of functions . The second case is Junge's recent Khintchine-type inequality for subspaces of the operator space R C, which he used to construct a cb-embedding of the operator Hilbert space OH into the predual of a hyperfinite factor. Also in this case, we obtain a sharp lower bound of . As a consequence, it follows that any subspace of a quotient of (R C)* is cb-isomorphic to a subspace of the predual of the hyperfinite factor of type III1, with cb-isomorphism constant . In particular, the operator Hilbert space OH has this property. |
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Keywords: | Noncommutative Khintchine-type inequalities Best constants Embedding of OH |
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