On the $\text{OUMD}$ property for the column Hilbert space $C$

Abstract

The operator space OUMD property was introduced by Pisier in the context of vector-valued noncommutative L p -spaces.It is an open problem whether the column Hilbert space has this property. Based on some complex interpolation techniques, we are able to relate this problem to the study of the OUMD q property for non-commutative L p -spaces.