Contractive projections and operator spaces

2002/01/21 by Matthew Neal, Bernard Russo
Mathematics · #math.OA #math.FA #msc:17C65 #msc:46l07

paper · pdf

published as Transactions of the AMS 355 No. 6 (2003) 2223-2262 · 40 pages, latex, the paper was submitted in October of 2000 and an announcement with the same title appeared in C. R. Acad. Sci. Paris 331 (2000), 873-878

arxiv created 2002/01/21 · arxiv updated 2009/11/30

Abstract

Parallel to the study of finite dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces H_n^k,0< k < n+1, generalizing the row and column Hilbert spaces R_n,C_n and show that an atomic subspace X of B(H) which is the range of a contractive projection on B(H) is isometrically completely contractive to a direct sum of the H_n^k and Cartan factors of types 1 to 4. In particular, for finite dimensional X, this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w*-closed JW*-triples without an infinite dimensional rank 1 w^*-closed ideal

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