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MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 953 MIXED-NORM INEQUALITIES AND OPERATOR SPACE LP EMBEDDING THEORY,MARIUS JUNGE,JAVIER PARCET by AMERICAN MATHEMATICAL SOCIETY, Marius Junge, Javier Parcet is a book available to read on EtoBox.

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Let $f_1, f_2, ldots, f_n$ be a family of independent copies of a given random variable $f$ in a probability space $(Omega, mathcal{F}, mu)$. Then, the following equivalence of norms holds whenever $1 le q le p < infty$, $$left( int_{Omega} left[ sum_{k=1}^n |f_k|^q right]^{p/q} d mu right)^{1/p} sim max_{r in {p,q}} left{ n^{1/r} left( int_Omega |f|^r dmu right)^{1/r} right}.$$ The authors prove a noncommutative analogue of this inequality for sums of free random variables over a given von Neumann subalgebra. This formulation leads to new classes of noncommutative function spaces which appear in quantum probability as square functions, conditioned square functions and maximal functions. Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.

Author

AMERICAN MATHEMATICAL SOCIETY, Marius Junge, Javier Parcet

Publisher

American Mathematical Society

Published

2009

Language

EN

ISBN

9780821846551

Subjects

Mathematics, Stem