Some remarks on smooth renormings of Banach spaces

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SYSNO ASEP	0476945
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Some remarks on smooth renormings of Banach spaces
Author(s)	Hájek, Petr Pavel (MU-W)_{RID, SAI} Russo, T. (IT)
Source Title	Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X Roč. 455, č. 2 (2017), s. 1272-1284
Number of pages	13 s.
Language	eng - English
Country	US - United States
Keywords	Fréchet smooth ; approximation of norms ; Ck-smooth norm
Subject RIV	BA - General Mathematics
OECD category	Pure mathematics
R&D Projects	GA16-07378S GA ČR - Czech Science Foundation (CSF)
Institutional support	MU-W - RVO:67985840
UT WOS	000406568800024
EID SCOPUS	85021216070
DOI	10.1016/j.jmaa.2017.05.077
Annotation	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.
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2018

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