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Smooth and polyhedral norms via fundamental biorthogonal systems
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SYSNO ASEP 0575126 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Smooth and polyhedral norms via fundamental biorthogonal systems Tvůrce(i) Dantas, S. (ES)
Hájek, P. (CZ)
Russo, Tommaso (MU-W) SAI, ORCIDZdroj.dok. International Mathematics Research Notices. - : Oxford University Press - ISSN 1073-7928
Roč. 2023, č. 16 (2023), s. 13909-13939Poč.str. 31 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Frechet differentiable norms ; Mazur intersection property ; Banach spaces Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GF20-22230L GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 000836338400001 EID SCOPUS 85168586630 DOI 10.1093/imrn/rnac211 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2024 Elektronická adresa https://doi.org/10.1093/imrn/rnac211
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