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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 6, Pages 207–222 (Mi izv59)  

This article is cited in 2 scientific papers (total in 2 papers)

Excessive maps, “arrival times” and perturbation of dynamical semigroups

A. S. Holevo

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The notion of excessive map for dynamical semigroup is introduced, and it is shown that an excessive map defines an operation-valued measure describing the measurement of an “arrival time” related to the irreversible dynamics described by the semigroup. Any such arrival time determines a positive perturbation of the dynamical semigroup describing the dynamics after “arrivals”. Generators of the relevant perturbations are characterized, and several examples, both commutative and a non-commutative, are discussed, elucidating the problem of standard representation.

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English version:
Izvestiya: Mathematics, 1995, 59:6, 1311–1325

Bibliographic databases:

MSC: 47D07, 46L55, 60J45
Received: 12.01.1995

Citation: A. S. Holevo, “Excessive maps, “arrival times” and perturbation of dynamical semigroups”, Izv. RAN. Ser. Mat., 59:6 (1995), 207–222; Izv. Math., 59:6 (1995), 1311–1325

Citation in format AMSBIB
\Bibitem{Hol95}
\by A.~S.~Holevo
\paper Excessive maps, ``arrival times'' and perturbation of dynamical semigroups
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 6
\pages 207--222
\mathnet{http://mi.mathnet.ru/izv59}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1481621}
\zmath{https://zbmath.org/?q=an:0877.47026}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 6
\pages 1311--1325
\crossref{https://doi.org/10.1070/IM1995v059n06ABEH000059}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UR47200010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Holevo, “There exists a non-standard dynamical semigroup on $\mathfrak L(\mathscr H)$”, Russian Math. Surveys, 51:6 (1996), 1206–1207  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. S. Kholevo, “Generatory kvantovykh odnomernykh diffuzii”, Teoriya veroyatn. i ee primen., 64:2 (2019), 308–327  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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