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Abstract
We prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained for stochastic one-parameter contiuous semigroups.
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Authors (2)
-
Krzysztof Bartoszek
- Uppsala University, Szwecja Department of Mathematics
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2017.03.068
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- Copyright (2017 Elsevier Inc.)
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
no. 452,
edition 2,
pages 1395 - 1412,
ISSN: 0022-247X - Language:
- English
- Publication year:
- 2017
- Bibliographic description:
- Bartoszek W., Bartoszek K.: A Noether theorem for stochastic operators on Schatten classes// JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. -Vol. 452, iss. 2 (2017), s.1395-1412
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jmaa.2017.03.068
- Verified by:
- Gdańsk University of Technology
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