Publication:
On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-Banach spaces

Consultable a partir de

2021-10-01

Date

2021

Authors

Ansorena, José L.
Wojtaszczyk, Przemyslaw

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

ES/1PE/MTM2016-76808-P

Abstract

We construct for each 0<p≤1 an infinite collection of subspaces of ℓp that extend the example of Lindenstrauss (Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12, 539–542, 1964) of a subspace of ℓ1 with no unconditional basis. The structure of this new class of p-Banach spaces is analyzed and some applications to the general theory of Lp-spaces for 0<p<1 are provided. The introduction of these spaces serves the purpose to develop the theory of conditional quasi-greedy bases in p-Banach spaces for p<1. Among the topics we consider are the existence of infinitely many conditional quasi-greedy bases in the spaces ℓp for p≤1 and the careful examination of the conditionality constants of the 'natural basis' of these spaces.

Keywords

Subspaces of ℓp, Banach spaces

Department

Estatistika, Informatika eta Matematika / Institute for Advanced Materials and Mathematics - INAMAT2 / Estadística, Informática y Matemáticas

Faculty/School

Degree

Doctorate program

Editor version

Funding entities

F. Albiac acknowledges the support of the Spanish Ministry for Economy and Competitivity under Grant MTM2016-76808-P as well as the Spanish Ministry for Science and Innovation under Grant PID2019-1077701GB-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. P. Wojtaszczyk was supported by National Science Centre, Poland Grant UMO-2016/21/B/ST1/00241.

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

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