Octahedrality and Gâteaux smoothness

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-16 DOI:10.1016/j.jmaa.2024.128968

Ch. Cobollo , P. Hájek

引用次数: 0

Abstract

We prove that every Banach space admitting a Gâteaux smooth norm and containing a complemented copy of

ℓ_{1}

has an equivalent renorming which is simultaneously Gâteaux smooth and octahedral. This is a partial solution to an open problem from the early nineties.

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八面体性和伽陀平滑性

我们证明，每一个容许高斯平滑规范并包含 ℓ1 的互补副本的巴拿赫空间都有一个等价的重规范，它同时是高斯平滑的和八面体的。这是九十年代初一个未决问题的部分解决方案。

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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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.