Measure of weak noncompactness and real interpolation of operators

A new measure of weak noncompactness is introduced. A logarithmic convexity-type result on the behaviour of this measure applied to bounded linear operators under real interpolation is proved. In particular, it gives a new proof of the theorem showing that if at least one of the operators T : A(i) --> B-i, i = 0, 1 is weakly compact, then so is T: A(theta ,p) --> B-theta ,B-p for all 0 < <theta> < 1 and 1 < p < <infinity>.