Structure of a Class of Operator-Selfdecomposable Probability Measures

Abstract

In 1972, K. Urbanik introduced the notion of operator-selfdecomposable probability measures (originally they were called Levy's measures). These measures are identified as limit distributions of partial sums of independent Banach space-valued random vectors normed by linear bounded operators. Recently, S. J. Wolfe has characterized the operator-selfdecomposable measures among the infinitely divisible ones. In this note we find examples of measures whose finite convolutions are a dense subset in a class of all operator-selfdecomposable ones.