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A Noether theorem for stochastic operators on Schatten classes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.ORCID iD: 0000-0002-5816-4345
Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland..
2017 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 2, 1395-1412 p.Article in journal (Refereed) Published
Abstract [en]

We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.

Place, publisher, year, edition, pages
2017. Vol. 452, no 2, 1395-1412 p.
Keyword [en]
Schatten classes, Markov operator, Noether property
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-322500DOI: 10.1016/j.jmaa.2017.03.068ISI: 000400224400039OAI: oai:DiVA.org:uu-322500DiVA: diva2:1103540
Funder
Swedish Institute, 00507/2012Swedish Institute, 11142/2013Swedish Institute, 19826/2014
Available from: 2017-05-30 Created: 2017-05-30 Last updated: 2017-05-30Bibliographically approved

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