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 $T:A_{0}\rightarrow B_{0}$ or $T:A_{1}\rightarrow B_{1}$ is weakly compact, then so is $T:A_{[\theta ]}\rightarrow B_{[\theta ]}$ for all $0\theta 1$, where $A_{[\theta ]}$ and $B_{[\theta ]}$ 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.
@article{10_4064_sm147_1_7,
author = {Andrzej Kryczka and Stanis{\l}aw Prus},
title = {Measure of weak noncompactness
under complex interpolation},
journal = {Studia Mathematica},
pages = {89--102},
year = {2001},
volume = {147},
number = {1},
doi = {10.4064/sm147-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm147-1-7/}
}
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AU - Andrzej Kryczka
AU - Stanisław Prus
TI - Measure of weak noncompactness
under complex interpolation
JO - Studia Mathematica
PY - 2001
SP - 89
EP - 102
VL - 147
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under complex interpolation
%J Studia Mathematica
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%P 89-102
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Andrzej Kryczka; Stanisław Prus. Measure of weak noncompactness
under complex interpolation. Studia Mathematica, Tome 147 (2001) no. 1, pp. 89-102. doi: 10.4064/sm147-1-7
