Smooth norms in dense subspaces of lp(G) and operator ranges

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00378788" target="_blank" >RIV/68407700:21230/24:00378788 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13163-023-00479-w" target="_blank" >https://doi.org/10.1007/s13163-023-00479-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-023-00479-w" target="_blank" >10.1007/s13163-023-00479-w</a>

Result language
angličtina
Original language name
Smooth norms in dense subspaces of lp(G) and operator ranges
Original language description
For 1 = p < 8, we prove that the dense subspace Y(p )of l(p)(G) comprising all elements y such that y ? l(q)(G) for some q ? (0, p) admits a C-8-smooth norm which locally depends on finitely many coordinates. Moreover, such a norm can be chosen as to approximate the ||.||(p)-norm. This provides examples of dense subspaces of l(p)(G) with a smooth norm which have the maximal possible linear dimension and are not obtained as the linear span of a biorthogonal system. Moreover, when p > 1 or G is countable, such subspaces additionally contain dense operator ranges; on the other hand, no non-separable operator range in l(1)(G) admits a C-1-smooth norm.
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
—
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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