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. ...
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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 /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
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.
