Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases
Date
2020
Version
Acceso abierto / Sarbide irekia
Type
Artículo / Artikulua
Version
Versión aceptada / Onetsi den bertsioa
Project Identifier
ES/1PE/MTM2016-76808-P
Impact
Abstract
We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, we give applications to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces. ...
[++]
Subject
Subsymmetric basis,
Garling sequence spaces,
Superreflexivity,
Besov spaces,
Conditional bases,
Conditionality constants,
Almost greedy bases
Publisher
Instytut Matematyczny
Published in
Studia Mathematica, 2020, 251(3), 277-288
Departament
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Publisher version
Sponsorship
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 Analisis Vectorial, multilineal, y aproximacion. F. Albiac was also supported by the grant MTM2016-76808-P (MINECO, Spain) for Operators, lattices, and structure of Banach spaces. S. J. Dilworth was supported by the National Science Foundation under Grant Number DMS-1361461. Denka Kutzarova acknowledges the support from Simmons Foundation Collaborative Grant Number 636954. S. J. Dilworth and D. Kutzarova were supported by the Workshop in Analysis and Probability at Texas A&M University in 2017.
