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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 232–241 (Mi mz3788)  

Von Neumann $J$-Algebras in a Space with Two Symmetries

M. S. Matveichuk

Kazan State University

Abstract: We show that a von Neumann $J$-algebra $\mathscr A$ of type $(\mathrm B)$ does not contain $J$-positive ($J$-negative) operators. $J$-projections in $\mathscr A$ are characterized. The class of plus-operators that are simultaneously self-adjoint and $J$-self-adjoint is described.

Keywords: von Neumann algebra, indefinite metric, plus-operator, $J$-algebra, Hilbert space, polar decomposition of an operator

DOI: https://doi.org/10.4213/mzm3788

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English version:
Mathematical Notes, 2007, 82:2, 203–211

Bibliographic databases:

UDC: 517.98
Received: 20.02.2003

Citation: M. S. Matveichuk, “Von Neumann $J$-Algebras in a Space with Two Symmetries”, Mat. Zametki, 82:2 (2007), 232–241; Math. Notes, 82:2 (2007), 203–211

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