Operator semi-selfdecomposable measures and related nested subclasses of measures on vector spaces

Abstract

$T$-semi-selfdecomposability and subclasses $L_m(b, Q)$ and $\tilde L_m(b, Q)$ of measures on complete separable metric vector spaces are introduced and basic properties are proved. In particular, we show that $μ$ is $T$-semi-selfdecomposable if and only if $μ= T(μ) ν$ where $ν$ is infinitely divisible and $μ$ is operator selfdecomposable if and only if $μ\in L_0(b, Q)$ for all $0< b < 1$.