Smooth and polyhedral norms via fundamental biorthogonal systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575126" target="_blank" >RIV/67985840:_____/23:00575126 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/23:00370646
Result on the web
<a href="https://doi.org/10.1093/imrn/rnac211" target="_blank" >https://doi.org/10.1093/imrn/rnac211</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnac211" target="_blank" >10.1093/imrn/rnac211</a>

Result language
angličtina
Original language name
Smooth and polyhedral norms via fundamental biorthogonal systems
Original language description
Let X be a Banach space with a fundamental biorthogonal system, and let y be the dense subspace spanned by the vectors of the system. We prove that y admits a C-infinity-smooth norm that locally depends on finitely many coordinates (LFC, for short), as well as a polyhedral norm that locally depends on finitely many coordinates. As a consequence, we also prove that y admits locally finite, sigma-uniformly discrete C-infinity-smooth and LFC partitions of unity and a C-1-smooth locally uniformly rotund norm. This theorem substantially generalises several results present in the literature and gives a complete picture concerning smoothness in such dense subspaces. Our result covers, for instance, every weakly Lindelof determined Banach space (hence, all reflexive ones), L-1 (mu) for every measure mu, l(infinity) (Gamma) spaces for every set Gamma, C(K) spaces where K is a Valdivia compactum or a compact Abelian group, duals of Asplund spaces, or preduals of Von Neumann algebras. Additionally, under Martin Maximum MM, all Banach spaces of density omega(1) are covered by our result.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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