 
Summary: EMBEDDINGS OF FINITE DIMENSIONAL OPERATOR SPACES
INTO THE SECOND DUAL
ALVARO ARIAS AND TIMUR OIKHBERG
Abstract. We show that, if a a finite dimensional operator space E is such
that X contains E Ccompletely isomorphically whenever X
contains E com
pletely isometrically, then E is 215
C11
completely isomorphic to RmCn, for some
n, m N {0}. The converse is also true: if X
contains Rm Cn completely
isomorphically, then X contains Rm Cn (2 + )completely isomorphically, for
any > 0.
1. Introduction
Local reflexivity of Banach spaces was first discovered by J. Lindenstrauss and
H. Rosenthal in [12]. Later, W. Johnson, H. Rosenthal, and M. Zippin [9] improved
on this result, and obtained:
Theorem 1.1. Suppose X is a Banach space, E and F are finite dimensional
subspaces of X
and X
