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Facially Symmetric Spaces and Predual Ones of Hermitian Part of von Neumann Algebras

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Abstract

We prove that predual of real part of von Neumann algebra is strongly facially symmetric space if and only if is it a direct sum of Abelian algebra and algebra of I2 type. At that, neutral strongly facially symmetric space is predual to Abelian algebra, only.

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Authors and Affiliations

  1. Karakalpak State University named after Berdakh, ul. Akademika C. Abdirova 1, Nukus, 230113, Republic of Uzbekistan

    M. M. Ibragimov & K. K. Kudaibergenov

  2. National University of Uzbekistan, ul. Durmon Yuli 29, Tashkent, 100125, Republic of Uzbekistan

    Zh. Kh. Seipullaev

Authors
  1. M. M. Ibragimov
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  2. K. K. Kudaibergenov
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  3. Zh. Kh. Seipullaev
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Corresponding author

Correspondence to M. M. Ibragimov.

Additional information

Original Russian Text © M.M. Ibragimov, K.K. Kudaibergenov, Zh.Kh. Seipullaev, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 5, pp. 33–40.

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Ibragimov, M.M., Kudaibergenov, K.K. & Seipullaev, Z.K. Facially Symmetric Spaces and Predual Ones of Hermitian Part of von Neumann Algebras. Russ Math. 62, 27–33 (2018). https://doi.org/10.3103/S1066369X18050055

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  • DOI: https://doi.org/10.3103/S1066369X18050055

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