巴拿赫空间中 (D) 型最大单调算子的表示法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-06-04 DOI:10.1007/s10957-024-02457-8

Bao T. Nguyen, Tran N. Nguyen, Huynh M. Hien

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引用次数: 0

摘要

本文涉及巴拿赫空间中的最大单调算子 A（D），其对偶空间是严格凸的。我们证明了 Ax 的面包含在算子在 x 附近点的有界网的所有弱（^*\）收敛极限的集合中，然后我们利用这个集合得到了 Ax 的表示。此外，我们还给出了基于算子在某些巴拿赫空间中的最小规范选择的 Ax 的支持函数的表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Representations for Maximal Monotone Operators of Type (D) in Banach Spaces

The present paper deals with a maximal monotone operator A of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value Ax at a given point x via its values at nearby points of x. We show that the faces of Ax are contained in the set of all weak\(^*\) convergent limits of bounded nets of the operator at nearby points of x, then we obtain a representation for Ax by use of this set. In addition, representations for the support function of Ax based on the minimal-norm selection of the operator in certain Banach spaces are given.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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