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Stochastic approximation properties in Banach spaces

V. P. Fonf, W. B. Johnson, G. Pisier, D. Preiss (2003)

Studia Mathematica

We show that a Banach space X has the stochastic approximation property iff it has the stochasic basis property, and these properties are equivalent to the approximation property if X has nontrivial type. If for every Radon probability on X, there is an operator from an L p space into X whose range has probability one, then X is a quotient of an L p space. This extends a theorem of Sato’s which dealt with the case p = 2. In any infinite-dimensional Banach space X there is a compact set K so that for...

Stochastic Banach principle in operator algebras

Genady Ya. Grabarnik, Laura Shwartz (2007)

Studia Mathematica

The classical Banach principle is an essential tool for the investigation of ergodic properties of Cesàro subsequences. The aim of this work is to extend the Banach principle to the case of stochastic convergence in operator algebras. We start by establishing a sufficient condition for stochastic convergence (stochastic Banach principle). Then we prove stochastic convergence for bounded Besicovitch sequences, and as a consequence for uniform subsequences.

Stochastic Dynamics of Quantum Spin Systems

Adam Majewski, Robert Olkiewicz, Bogusław Zegarliński (1998)

Banach Center Publications

We show that recently introduced noncommutative L p -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second, the tempered-stratified...

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