On lattice-almost isometric copies of $$c_0(\Gamma )$$ and $$\ell _1(\Gamma )$$ in Banach lattices

Autor:	Andrés Fabián Leal-Archila, Michael A. Rincón-Villamizar
Rok vydání:	2021
Předmět:	Distortion (mathematics) Physics Combinatorics Mathematics::Functional Analysis Mathematics::Operator Algebras Astrophysics::High Energy Astrophysical Phenomena General Mathematics Lattice (order) Banach lattice Uncountable set Algebra over a field
Zdroj:	Rendiconti del Circolo Matematico di Palermo Series 2. 71:515-523
ISSN:	1973-4409 0009-725X
DOI:	10.1007/s12215-021-00620-y
Popis:	The main aim of this paper is proving the corresponding lattice version of James distortion theorem for $$c_0(\Gamma )$$ and $$\ell _1(\Gamma )$$ : if a Banach lattice contains lattice copy of $$c_0(\Gamma )$$ ( $$\ell _1(\Gamma )$$ respectively), then it contains lattice-almost isometric copies of $$c_0(\Gamma )$$ ( $$\ell _1(\Gamma )$$ respectively). We also show that the classical Lozanovskii and Meyer-Nieberg Theorem for $$c_0$$ is not longer valid for $$c_0(\Gamma )$$ whenever $$\Gamma $$ is uncountable.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::66954ffd98d80690ff52c5ed07e2952f https://doi.org/10.1007/s12215-021-00620-y Zobrazit plný text záznamu Full text from SpringerLink