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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 350–361 (Mi mz111)  

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

Some Properties of a Class of Diagonalizable States of von Neumann Algebras

N. N. Ganikhodzhaev, F. M. Mukhamedov

National University of Uzbekistan named after M. Ulugbek

Abstract: In this paper, a class of representations of uniformly hyperfinite algebras is constructed and the corresponding von Neumann algebras are studied. It is proved that, under certain conditions, the Markov states generate factors of type $\operatorname{III}_\lambda$, where $\lambda\in(0,1)$, in the GNS representation; this gives a negative answer to the conjecture that the factors corresponding to Hamiltonians with nontrivial interactions have type $\operatorname{III}_1$. It is shown that, for a certain class of Hamiltonians, there exists a unique translation-invariant ground state.

DOI: https://doi.org/10.4213/mzm111

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English version:
Mathematical Notes, 2004, 76:3, 329–338

Bibliographic databases:

UDC: 517.98
Received: 17.06.2001
Revised: 20.11.2003

Citation: N. N. Ganikhodzhaev, F. M. Mukhamedov, “Some Properties of a Class of Diagonalizable States of von Neumann Algebras”, Mat. Zametki, 76:3 (2004), 350–361; Math. Notes, 76:3 (2004), 329–338

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mukhamedov F. Barhoumi A. Souissi A., “Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree”, J. Stat. Phys., 163:3 (2016), 544–567  crossref  mathscinet  zmath  isi  elib  scopus
    2. Accardi L. Mukhamedov F. Souissi A., “On Construction of Quantum Markov Chains on Cayley trees”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, ed. Ayupov S. Chilin V. Ganikhodjaev N. Mukhamedov F. Rakhimov I., IOP Publishing Ltd, 2016, 012018  crossref  isi  scopus
  • Математические заметки Mathematical Notes
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