Abstract:
In the paper we study the asymptotic ratio set (an invariant for von Neumann algebras introduced by H. Araki and E. J. Woods) with the aid of spectral properties of modular operators of the von Neumann algebra. We give an equivalent description of this set in terms of modular operators and indicate a constructive method for its evaluation.
Bibliography: 19 items.
\Bibitem{Gol75}
\by V.~Ya.~Golodets
\paper Spectral properties of modular operators and the asymptotic ratio set
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 599--619
\mathnet{http://mi.mathnet.ru/eng/im2044}
\crossref{https://doi.org/10.1070/IM1975v009n03ABEH001492}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=380437}
\zmath{https://zbmath.org/?q=an:0312.46079}
Linking options:
https://www.mathnet.ru/eng/im2044
https://doi.org/10.1070/IM1975v009n03ABEH001492
https://www.mathnet.ru/eng/im/v39/i3/p635
This publication is cited in the following 4 articles:
V. Ya. Golodets, N. I. Nessonov, “Asymptotic algebra and outer conjugacy classes of automorphisms of factors”, Math. USSR-Izv., 16:3 (1981), 457–477
V. Ya. Golodets, “Automorphism of von Neumann algebras and approximatively finite type III1 factors with an almost-periodic weight”, Funct. Anal. Appl., 14:2 (1980), 123–125
V. Ya. Golodets, N. I. Nessonov, “Invariant states on asymptotically Abelian factors of type III”, Funct. Anal. Appl., 13:2 (1979), 141–142
V. Ya. Golodets, “Modular operators and asymptotic commutativity in von Neumann algebras”, Russian Math. Surveys, 33:1 (1978), 47–106
Citation in format AMSBIB
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