Brief communications

Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part

Sh. A. Ayupov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: In this note we describe (up to isomorphism) the real von Neiman algebras $R$ with Abelian skew-symmetric part $R_k=\{x\in R:x^*=-x\}$, i.e., such that $xy-yx=0$ for any $x,y\in R_k$.

Keywords: real von Neimann algebra, symmetric element, skew-symmetric element, $JW$-algebra, spin factor.

UDC: 517.98

Received: 07.05.2001

DOI: 10.4213/faa193

 English version: Functional Analysis and Its Applications, 2002, 36:2, 145–147

Bibliographic databases:

• 
• 
• 
•