Transfer Principles, Fenchel Conjugate, and Subdifferential Formulas in Fan-Theobald-von Neumann Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-18 DOI:10.1007/s10957-024-02474-7

Juyoung Jeong, M. Seetharama Gowda

引用次数: 0

Abstract

A Fan-Theobald-von Neumann system [7] is a triple \((\mathcal {V},\mathcal {W},\lambda )\), where \(\mathcal {V}\) and \(\mathcal {W}\) are real inner product spaces and \(\lambda :\mathcal {V}\rightarrow \mathcal {W}\) is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decomposition systems (Eaton triples). The present article is a continuation of [9] where the concepts of commutativity, automorphisms, majorization, and reduction were introduced and elaborated. Here, we describe some transfer principles and present Fenchel conjugate and subdifferential formulas.

查看原文本刊更多论文

范-特奥伯德-冯-诺依曼系统中的转移原理、芬切尔共轭和次微分公式

一个Fan-Theobald-von Neumann系统[7]是一个三元组((\mathcal {V},\mathcal {W},\lambda )\), 其中\(\mathcal {V}\) 和\(\mathcal {W}\)是实内积空间，\(\lambda ：\)是一个保留规范的映射，它满足范-特奥贝尔-冯-诺依曼类型的不等式以及相等的条件。例子包括欧几里得乔丹代数、某些双曲多项式诱导的系统和正则分解系统（伊顿三元组）。本文是[9]的继续，[9]中介绍并阐述了交换性、自动态、大化和还原等概念。在此，我们介绍了一些转移原理，并提出了芬切尔共轭公式和子微分公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.