  The concept of uniform convexity of a Banach space was generalized to linear
operators between Banach spaces and studied by Beauzamy [1976]. Under this
generalization, a Banach space X is uniformly convex if and only if its
identity map I_X is. Pisier showed that uniformly convex Banach spaces have
martingale type p for some p>1. We show that this fact is in general not true
for linear operators. To remedy the situation, we introduce the new concept of
martingale subtype and show, that it is equivalent, also in the operator case,
to the existence of an equivalent uniformly convex norm on X. In the case of
identity maps it is also equivalent to having martingale type p for some p>1.
  Our main method is to use sequences of ideal norms defined on the class of
all linear operators and to study the factorization of the finite summation
operators. There is a certain analogy with the theory of Rademacher type.
