求范数算子与变分原理

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-05-12 DOI:10.4064/sm210628-6-9

M. Bachir

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引用次数: 3

摘要

.我们建立了一个线性变分原理，推广了Deville–Godefroy–Zizler的变分原理。我们用这个变分原理证明了如果X是一个具有Schachermayer性质（α）的Banach空间，并且Y是任何Banach空间时，则从X到Y的所有强范数线性算子的集合是σ-多孔集合的补集。此外，我们将我们的结果应用于一类抽象的（线性和非线性）算子空间。

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Norm attaining operators and variational principle

. We establish a linear variational principle extending Deville–Godefroy– Zizler’s one. We use this variational principle to prove that if X is a Banach space having property ( α ) of Schachermayer and Y is any Banach space, then the set of all strongly norm attaining linear operators from X into Y is the complement of a σ -porous set. Moreover, we apply our results to an abstract class of (linear and nonlinear) operator spaces.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.