Journal of Operator Theory

Volume 51, Issue 2, Spring 2004 pp. 281-301.

Normal contractive projections preserve type

Authors: Cho-Ho Chu, (1) Matthew Neal (2) and Bernard Russo (3)
Author institution: (1) School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK
(2) Department of Mathematics, Denison University, Granville, Ohio 43023, USA
(3) Department of Mathematics, University of California, Irvine, California 92697--3875, USA

Summary: Given a ${\rm JBW}^*$-triple $Z$ and a normal contractive projection $P:Z\rightarrow Z$, we show that the (Murray-von Neumann) type of each summand of $P(Z)$ is dominated by the type of $Z$.

Keywords: Contractive projection, JB*-triple, von Neumann algebra, Murray--von Neumann classification

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