Uniqueness of dilation invariant norms

被引:3
|
作者
Moreno, E [1 ]
Villena, AR [1 ]
机构
[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain
关键词
D O I
10.1090/S0002-9939-04-07327-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let delta(a) be a nontrivial dilation. We show that every complete norm parallel to.parallel to on L-1(R-N) that makes delta(a) from (L-1(R-N); parallel to.parallel to) into itself continuous is equivalent to parallel to.parallel to(1.)delta(a) also determines the norm of both C-0(R-N) and L-p(R-N) with 1 < p < infinity in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on L-infinity(R-N).
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页码:2067 / 2073
页数:7
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