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: A₀ → B₀ or T: A₁ → B₁ is weakly compact, then so is for all 0 < θ < 1, where and are interpolation spaces with respect to the pairs (A₀,A₁) and (B₀,B₁). Some formulae for this measure and relations to other quantities measuring weak noncompactness are established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-1-7,
author = {Andrzej Kryczka and Stanis\l aw Prus},
title = {Measure of weak noncompactness under complex interpolation},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {89-102},
zbl = {0995.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-1-7}
}
Andrzej Kryczka; Stanisław Prus. Measure of weak noncompactness under complex interpolation. Studia Mathematica, Tome 147 (2001) pp. 89-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-1-7/