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

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 I 2 type. At that, neutral strongly facially symmetric space is predual to Abelian algebra, only.

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Veröffentlicht in:Russian mathematics 2018-05, Vol.62 (5), p.27-33
Hauptverfasser: Ibragimov, M. M., Kudaibergenov, K. K., Seipullaev, Zh. Kh
Format: Artikel
Sprache:eng
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Zusammenfassung: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 I 2 type. At that, neutral strongly facially symmetric space is predual to Abelian algebra, only.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X18050055