Vol. 205, No. 1, 2002

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

Ping Wong Ng and Narutaka Ozawa

Vol. 205 (2002), No. 1, 171–195

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 pRq 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.

Received: 14 February 2000
Revised: 16 October 2001
Published: 1 July 2002
Ping Wong Ng
Department of Mathematics
University of Toronto
Toronto, Ontario
Canada M5S 3G3
Narutaka Ozawa
Department of Mathematical Science
University of Tokyo
Komaba 153-8914, Japan