On strongly condensing operators

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• 作者：Nina A. Erzakova ; Martin Väth
• 关键词：Positively homogeneous map ; Measure of noncompactness ; Fréchet derivative ; Asymptotic derivative ; Compactness ; Weak compactness ; Superposition operator ; Ideal space of measurable functions ; Regular space of measurable functions ; Lebesgue space ; Lorentz space ; Orlicz space
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：309-323
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

Given a set-function \(\psi \) defined on bounded subsets of a Banach space with certain properties, necessary and sufficient criteria for \(\psi (A(U))=0\) are given, when A is positively homogeneous of some order and U is bounded. The results are applied to give necessary and sufficient criteria for the compactness and weak compactness of a Fréchet derivative (in some point or at \(\infty \)) and when an operator is improving.