On a certain class of semigroups of operators

Details On a certain class of semigroups of operators On a certain class of semigroups of operators

2010-10-28

arxiv.org/abs/1010.5925v2

Physics

Mathematical Physics

11 pages

Scientific paper

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.

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