Some remarks on smooth renormings of Banach spaces

0476945 - MÚ 2018 RIV US eng J - Journal Article
Hájek, Petr Pavel - Russo, T.
Some remarks on smooth renormings of Banach spaces.
Journal of Mathematical Analysis and Applications. Roč. 455, č. 2 (2017), s. 1272-1284. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA16-07378S
Institutional support: RVO:67985840
Keywords : Fréchet smooth * approximation of norms * Ck-smooth norm
OECD category: Pure mathematics
Impact factor: 1.138, year: 2017
http://www.sciencedirect.com/science/article/pii/S0022247X17305462?via%3Dihub

We prove that in every separable Banach space X with a Schauder basis and a Ck-smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a Ck-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.
Permanent Link: http://hdl.handle.net/11104/0273350