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Automorphisms of spectral lattices of unbounded positive operators

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Abstract

We introduce and study spectral order on unbounded operators. Main result of this note characterizes spectral order automorphism of the lattice of positive (possibly unbounded) self-adjoint operators.

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References

  1. T. Ando, Linear Algebra and Its Applications 118, 163 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  2. W. Arveson, J. of Functional Analysis 15, 217 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  3. P. A. Fillmore and W. E. Longstaff, Can. J. Math. XXXVI(5), 820 (1984).

    Article  MathSciNet  Google Scholar 

  4. H. F. de Groote, On the canonical lattice structure on the effect algebra of a von Neumann algebra, arXiv: math-ph/0410018v1 6 Oct 2004.

    Google Scholar 

  5. J. Hamhalter, Quantum Measure Theory (Kluwer Academic Publishers, Dordrecht, Boston, London, 2003), Book Series: Fundamental Theories of Physics, Vol. 134, p. 418, ISBN 1-4020-1714-6

    Book  MATH  Google Scholar 

  6. J. Hamhalter, J. Math. Anal. Appl. 331, 1122 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Hamhalter, Int. J. Theor. Phys. 47, 245 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. V. Kadison, Proc. Amer. Math. Soc. 2, 505 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Kato, Linear and Multilinear Algebra 8, 15 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Molnar and P. Šemrl, Leters in Mathematical Physics 80, 239 (2007).

    Article  MATH  Google Scholar 

  11. M. P. Olson, Proc. Amer. Math. Soc. 28(2), 537 (1971).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Statistics, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kremlevskaya ul. 18, Kazan, 420008, Russia

    E. Turilova

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  1. E. Turilova
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Correspondence to E. Turilova.

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Submitted by A. V. Lapin

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Turilova, E. Automorphisms of spectral lattices of unbounded positive operators. Lobachevskii J Math 35, 259–263 (2014). https://doi.org/10.1134/S1995080214030111

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  • DOI: https://doi.org/10.1134/S1995080214030111

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