Domains of operator semi-attraction of probability measures on Banach spaces

Abstract

The paper deals with operator (semi-) stability and domains of operator (semi-) attraction of probability measures on infinite dimensional Banach spaces: characterizations of operator (semi-) stability and of domains of (normal) operator (semi-) attraction are given; it is shown that the set of operator stable probability measures is a closed subset under weak topology; the domain of operator semi-attraction of a given stable probability measure coincides with its domain of operator attraction; and a probability measure is (semi-) stable iff its finite-dimensional projections are (semi-) stable.