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 : Ai -» Bi, i = 0,1 is weakly compact, then so is T : A g
We introduce and study the class of nearly uniformly noncreasy Banach spaces. It is proved that they have the weak fixed point property. A stability result for this property is obtained.
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