Contractive projections and operator spaces
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
Cite
@article{arxiv.math/0201187,
title = {Contractive projections and operator spaces},
author = {Matthew Neal and Bernard Russo},
journal= {arXiv preprint arXiv:math/0201187},
year = {2007}
}
Comments
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