Abstract
An operator-decomposable Gaussian measure on a separable Banach space can be factorized into a convolution product of a strongly operator-decomposable Gaussian measure and an operator-invariant Gaussian measure (with respect to the same operator). An example for this very factorization is discussed in some detail. In particular it is shown that a strongly operator-decomposable Gaussian measure need not necessarily be supported by the contraction subspace of the operator involved. Finally, the decomposability semigroup of a Gaussian measure turns out to be convex; and the corresponding invariance semigroup belongs to its extreme boundary.
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Siebert, E. Operator-decomposability of Gaussian measures on separable Banach spaces. J Theor Probab 5, 333–347 (1992). https://doi.org/10.1007/BF01046739
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DOI: https://doi.org/10.1007/BF01046739