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.

UDC: 517.98

Received: 20.02.2003

DOI: 10.4213/mzm3788

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

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