Measure of weak noncompactness under complex interpolation

Andrzej Kryczka, Stanisław Prus
2001 Studia Mathematica  
Logarithmic convexity of a measure of weak noncompactness for bounded linear operators under Calderón's complex interpolation is proved. This is a quantitative version for weakly noncompact operators of the following: if T : and B [θ] are interpolation spaces with respect to the pairs (A 0 , A 1 ) and (B 0 , B 1 ). Some formulae for this measure and relations to other quantities measuring weak noncompactness are established.
doi:10.4064/sm147-1-7 fatcat:26fltxj6wje3to3f3wkamkv7ne