Statistically strongly regular matrices and some core theorems.
Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.
Let be an entire self-map of , be an entire function on and be a vector-valued entire function on . We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator as follows: We investigate the boundedness and compactness of on Fock spaces. The complex symmetry and self-adjointness of are also characterized.
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 space into X whose range has probability one, then X is a quotient of an 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...
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.
We show that recently introduced noncommutative -spaces can be used to constructions of Markov semigroups for quantum systems on a lattice.