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
收藏
页码：389 / 401
页数：13
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