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This article is cited in 3 scientific papers (total in 3 papers)
Maps with separable dynamics and the spectral properties of the operators generated by them
A. B. Antonevichab, A. A. Ahmatovaa, Ju. Makowskab a Belarusian State University, Minsk
b University of Bialystok
Abstract:
A map $\alpha $ of a space $X$ into itself generates weighted shift operators $B$ in function spaces on $X$. The spectral properties of such operators are intimately connected with the dynamics of $\alpha$. It was known previously that the spectrum of an operator depends only on the set of invariant ergodic measures for $\alpha$. Conditions for the right invertibility of the operators $B-\lambda I$ are obtained when $\lambda$ is a spectral value. The main result states that right invertibility is only possible when a nontrivial attractor exists.
Bibliography: 29 titles.
Keywords:
spectrum of an operator, one-sided invertibility, essential spectrum, attractor, ergodic measure.
Received: 05.02.2014 and 09.12.2014
Citation:
A. B. Antonevich, A. A. Ahmatova, Ju. Makowska, “Maps with separable dynamics and the spectral properties of the operators generated by them”, Mat. Sb., 206:3 (2015), 3–34; Sb. Math., 206:3 (2015), 341–369
Linking options:
https://www.mathnet.ru/eng/sm8340https://doi.org/10.1070/SM2015v206n03ABEH004461 https://www.mathnet.ru/eng/sm/v206/i3/p3
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Abstract page: | 580 | Russian version PDF: | 166 | English version PDF: | 17 | References: | 48 | First page: | 36 |
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