Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

Abstract.

T-semi-selfdecomposability, operator selfdecomposability, and subclasses L _m (b, (T _t )) and \({\tilde L}_m (b, (T_t))\) 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∈L₀(b, (T _t )) for all 0 < b < .