Measure of weak noncompactness and real interpolation of operators

被引：33

作者：

Kryczka, A ^{[1
]}

Prus, S ^{[1
]}

Szczepanik, M ^{[1
]}

机构：

[1] Marie Curie Sklodowska Univ, Inst Math, PL-20031 Lublin, Poland

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2000年 / 62卷 / 03期

关键词：

D O I：

10.1017/S0004972700018906

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 : A(i) --> B-i, i = 0, 1 is weakly compact, then so is T: A(theta ,p) --> B-theta ,B-p for all 0 < <theta> < 1 and 1 < p < <infinity>.

引用

页码：389 / 401

页数：13

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