On the permutative equivalence of squares of unconditional bases
Date
2022Version
Acceso abierto / Sarbide irekia
Type
Artículo / Artikulua
Version
Versión publicada / Argitaratu den bertsioa
Project Identifier
Impact
|
10.1016/j.aim.2022.108695
Abstract
We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given ...
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We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. Among the main applications of this principle we obtain the uniqueness of unconditional basis up to permutation of finite sums of spaces with this property, as well as the first addition to the scant list of the known Banach spaces with a unique unconditional bases up to permutation since [14]. [--]
Subject
Banach lattice,
Quasi-Banach spaces,
Uniqueness of unconditional basis
Publisher
Elsevier
Published in
Advances in Mathematics 410 (2022) 108695
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
Both authors supported by the Spanish Ministry for Science, Innovation, and Universities, Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Approximación. The first-named author also acknowledges the support from Spanish Ministry for Science and Innovation, Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces.