Contractive projections and operator spaces

Details Contractive projections and operator spaces Contractive projections and operator spaces

2002-01-21

arxiv.org/abs/math/0201187v1

Transactions of the AMS 355 No. 6 (2003) 2223-2262

Mathematics

Operator Algebras

40 pages, latex, the paper was submitted in October of 2000 and an announcement with the same title appeared in C. R. Acad. Sc

Scientific paper

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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