Some remarks on smooth renormings of Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Hajek, Petr^1,2  Russo, Tommaso³ 

[1] Czech Acad Sci, Math Inst, Zitna 25, Prague 11567 1, Czech Republic

[2] Czech Tech Univ, Dept Math, Fac Elect Engn, Zikova 4, Prague 16000, Czech Republic

[3] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy

关键词: Frechet smooth;    C-k-smooth norm;    Approximation of norms;    Minkowski functional;    Renorming;    Implicit function theorem;   

DOI  :  10.1016/j.jmaa.2017.05.077

来源: Elsevier

【 摘 要 】

We prove that in every separable Banach space X with a Schauder basis and a C-k-smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a C-k-smooth one in a way that the approximation is improving as fast as we wish on the elements depending only on the tail of the Schauder basis. Our result solves a problem from the recent monograph of Guirao, Montesinos and Zizler. (C) 2017 Published by Elsevier Inc.

【 授权许可】

Free