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Título: Mixed-Norm Inequalities And Operator Space L_p Embedding Theory | |
| Autor: Junge Marius/ Parcet Javier | Precio: $935.61 | |
| Editorial: American Mathematical Society | Año: 2009 | |
| Tema: Matematicas, Textos, Teorias | Edición: 1ª | |
| Sinopsis | ISBN: 9780821846551 | |
| 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, ( \int_{\Omega}[ \sum_{k=1}^n |f_k|^q ]^{p/q} d \mu )^{1/p} \sim \max_{r \in \{p,q\}} \{ n^{1/r}( \int_\Omega |f|^r d\mu)^{1/r} \}. 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.
Table of Contents Introduction Noncommutative integration Amalgamated L_p spaces An interpolation theorem Conditional L_p spaces Intersections of L_p spaces Factorization of \mathcal {J}_{p,q}^n(\mathcal {M}, \mathsf {E}) Mixed-norm inequalities Operator space L_p embeddings Bibliography |
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Última actualización: Jul 2019