Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p ≤ 1
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p ≤ 1 over the Euclidean spaces Rd and Zd. To that end, on one hand we show that Fp(Rd) admits a Schauder basis for every p ∈ 2 (0, 1], thus generalizing the corresponding result for the case p = 1 by H_ajek and Perneck_a [20, Theorem 3.1] and answering in the positive a question that was raised in . Expl ... [++]
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p ≤ 1 over the Euclidean spaces Rd and Zd. To that end, on one hand we show that Fp(Rd) admits a Schauder basis for every p ∈ 2 (0, 1], thus generalizing the corresponding result for the case p = 1 by H_ajek and Perneck_a [20, Theorem 3.1] and answering in the positive a question that was raised in . Explicit formulas for the bases of both Fp(Rd) and its isomorphic space Fp([0, 1]d) are given. On the other hand we show that the well-known fact that F(Z) is isomorphic to l1 does not extend to the case when p < 1, that is, Fp(Z) is not isomorphic to lp when 0 < p < 1. [--]
Isomorphic theory of Banach spaces, Lp-space, Lipschitz free p-space, Lipschitz free space, Quasi-Banach space, Schauder basis
Collectanea Mathematica (2021)
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas / Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila / Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
F. Albiac acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces. F. Albiac and J. L. Ansorena acknowledge the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación. M. Cúth has been supported by Charles University Research program No. UNCE/SCI/023. M. Doucha was supported by the GAČR project EXPRO 20-31529X and RVO: 67985840.
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Albiac Alesanco, Fernando José ; Ansorena, José L.; Cúth, Marek; Doucha, Michal (American Mathematical Society, 2021) Artículo / ArtikuluaWe find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free ...
Albiac Alesanco, Fernando José ; Leránoz Istúriz, María Camino (Hindawi Publishing Corporation, 2009) Artículo / ArtikuluaWe show that the p-convexified Tsirelson space tau((p)) for 0 < p < 1 and all its complemented subspaces with unconditional basis have unique unconditional basis up to permutation. The techniques involved in the proof are ...
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