Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 28, No 3, (2002), 201p-206p
Abstract:
Let X be a closed subspace of B(H) for some Hilbert space
H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] =
(S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X)
and showed that there are p−matricially normed spaces. In this paper we
prove that conversely, if X is a p−matricially normed space with p = 1,
then there is an operator structure on X, such that M1,n (X) = S1 [X] where
Sn,1 [X] is the finite dimentional version of S1 [X]. For p = 1, we have no
answer.
