Uniqueness of translation invariant norms

被引:14
|
作者
Jarosz, K [1 ]
机构
[1] So Illinois Univ, Dept Math & Stat, Edwardsville, IL 62026 USA
关键词
automatic continuity; uniqueness of norm; translation invariant functionals;
D O I
10.1006/jfan.2000.3593
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let A be a Banach function space and let M be a family of multipliers on A. We provide conditions on M so that the original topology of A is the only complete norm topology on A making all of the maps from M continuous. As a corollary we show that for a compact abelian group G, and a circle group T for A = L-P(T)(-), 1 < p < infinity, the L-P-norm is the only one that makes all trans rations continuous, while for A = C(G), A = L-infinity(G), or A = L-1(G) there are other norms with that property. For noncompact groups the situation is different-on the space L-1(R) the L-1-norm is the only one that makes a single nontrivial translation continuous. (C) 2000 Academic Press.
引用
收藏
页码:417 / 429
页数:13
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