Octahedrality and Gâteaux smoothness

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications 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

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.