关于非中点局部均匀圆的光滑圆范数的注释

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-02 DOI:10.1016/j.jmaa.2025.129544

Carlo Alberto De Bernardi , Alessandro Preti , Jacopo Somaglia

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引用次数: 0

摘要

证明了每一个可分离无限维Banach空间都存在一个非中点局部一致圆的g teaux光滑圆范数。此外，利用类似的技术，在具有可分离对偶的无限维Banach空间中，我们给出了一个非中点局部一致圆的fr光滑弱一致圆范数。这两个结果对a . J. Guirao、V. Montesinos和V. Zizler的一些开放性问题给出了肯定的回答。

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A note on smooth rotund norms which are not midpoint locally uniformly rotund

We prove that every separable infinite-dimensional Banach space admits a Gâteaux smooth and rotund norm which is not midpoint locally uniformly rotund. Moreover, by using a similar technique, we provide in every infinite-dimensional Banach space with separable dual a Fréchet smooth and weakly uniformly rotund norm which is not midpoint locally uniformly rotund. These two results provide a positive answer to some open problems by A. J. Guirao, V. Montesinos, and V. Zizler.

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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.