ON THE CLASS OF OPERATOR STABLE DISTRIBUTIONS IN A
SEPARABLE BANACH SPACE
Abstract: This paper characterizes the class of all limit probability measures of
normalized and centralized convolution powers in a separable Banach space which are
defined by
for
some linear and bounded operators
and some shifts
It is shown that this class
coincides with the set of all infinitely divisible laws in
provided that
is infinite
dimensional.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -