Geodesic
Measure of weak noncompactness under complex interpolation
Andrzej Kryczka 1   ; Stanisław Prus 1
1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland
Studia Mathematica, Tome 147 (2001) no. 1, pp. 89-102 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm147-1-7
Keywords: logarithmic convexity measure weak noncompactness bounded linear operators under calder complex interpolation proved quantitative version weakly noncompact operators following rightarrow rightarrow weakly compact theta rightarrow theta theta where theta theta interpolation spaces respect pairs formulae measure relations other quantities measuring weak noncompactness established

Andrzej Kryczka  1   ; Stanisław Prus  1

1 Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland 
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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

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