Smooth norms in dense subspaces of Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346250" target="_blank" >RIV/68407700:21230/20:00346250 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2020.123963" target="_blank" >https://doi.org/10.1016/j.jmaa.2020.123963</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2020.123963" target="_blank" >10.1016/j.jmaa.2020.123963</a>

Result language
angličtina
Original language name
Smooth norms in dense subspaces of Banach spaces
Original language description
In the first part of our paper, we show that too has a dense linear subspace which admits an equivalent real analytic norm. As a corollary, every separable Banach space, as well as ti (c), also has a dense linear subspace which admits an analytic renorming. By contrast, no dense subspace of ce(Loi) admits an analytic norm. In the second part, we prove (solving in particular an open problem of Guirao, Montesinos, and Zizler in [7]) that every Banach space with a long unconditional Schauder basis contains a dense subspace that admits a C -smooth norm. Finally, we prove that there is a proper dense subspace of 2,c,o(w1) that admits no Gateaux smooth norm. (Here, Ego (cal) denotes the Banach space of real-valued, bounded, and countably supported functions on col.) (C) 2020 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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