Contractive projections and operator spaces
Parallel to the study of finite dimensional Banach spaces,
there is a growing interest in the corresponding local theory of
operator spaces. We introduce a family of Hilbertian operator spaces
H(n,k), 1,2,...,n, generalizing the row and column Hilbert spaces and
show that a reflexive subspace of the bounded operators on a Hilbert
space which is the range of a contractive projection 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 subspaces, this
answers a question posed by Oikhberg and Rosenthal in their study of
extension properties of the space of compact operators.
(This paper has appeared in Comptes Rendus Acad. Sci. Paris 331 (2000),
873-878,
AND Trans. Amer. Math. Soc.355
(2003), 2223-2262)
Matthew Neal < mneal@math.uci.edu >
Bernard Russo < brusso@math.uci.edu >