A characterization of completely 1-complemented subspaces of noncommutative L₁-spaces

Ping Wong Ng and Narutaka Ozawa

Vol. 205 (2002), No. 1, 171–195

DOI: 10.2140/pjm.2002.205.171

Abstract

A ternary ring of operators is an “off-diagonal corner” of a C^∗-algebra and the predual of a ternary ring of operators (if it exists) is of the form pR_∗q for some von Neumann algebra R and projections p and q in R. In this paper, we prove that a subspace of the predual of a ternary ring of operators is completely 1-complemented if and only if it is completely isometrically isomorphic to the predual of some ternary ring of operators. We next give an operator space characterization of the preduals of separable injective von Neumann algebras. Finally, we prove some concrete results about the finite dimensional completely 1-complemented subspaces of a von Neumann algebra predual.

Milestones

Received: 14 February 2000

Revised: 16 October 2001

Published: 1 July 2002