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On the Structure of Covariant Dynamical Semigroups

✍ Scribed by A.S. Holevo

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
741 KB
Volume
131
Category
Article
ISSN
0022-1236

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✦ Synopsis

Dynamical semigroups in (\mathfrak{B}(\mathscr{H})) without the norm-continuity assumption are investigated by introducing the notion of form-generator. giving the mathematical expression for the idea of Markovian master equation. It is shown that any formgenerator on (\mathfrak{B}(\mathscr{H})) admits a standard representation, and the non-uniqueness of this representation is described. The equations for the components of the standard representation of a covariant form-generator are deduced in terms of low-order cohomology of the symmetry group; in particular, noncommutative LevyKhinchin-type formulae for the shift-covariant form-generators are obtained. Relations with previous works on characterisation of the (unbounded) generator of a dynamical semigroup are discussed. ir. 1995 Academic Press, Inc.

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