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.
"Structure of a Class of Operator-Selfdecomposable Probability Measures." Ann. Probab. 10 (3) 849 - 856, August, 1982. https://doi.org/10.1214/aop/1176993796