A group invariant Bishop-Phelps theorem,Proceedings of the American Mathematical Society

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A group invariant Bishop-Phelps theorem
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-02-05 , DOI: 10.1090/proc/15321
Javier Falcó

Abstract:We show that for any Banach space and any compact topological group $G\subset L(X)$ such that the norm of

-invariant, the set of norm attaining

-invariant functionals on

is dense in the set of all

-invariant functionals on

, where a mapping

is called

-invariant if for every $x\in X$ and every $g\in G$ , $f\big (g(x)\big )=f(x)$ . In contrast, we show also that the analog of Bollobás result does not hold in general. A version of Bollobás and James' theorems is also presented.

中文翻译：

群不变Bishop-Phelps定理

摘要：我们表明，任何的Banach空间和任何紧凑型拓扑群这样的规范是-invariant，实现了一套规范的-invariant函上是集合所有的密集上-invariant函，其中映射被称为-如果每个都不变，。相比之下，我们还表明，Bollobás结果的类似物通常不成立。还介绍了Bollobás和James定理的一个版本。 $G \子集L（X）$

$x \ in X$ $g \ in G$ $f \ big（g（x）\ big）= f（x）$

更新日期：2021-04-12

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