Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases
| Autor: | Denka Kutzarova, Stephen J. Dilworth, Fernando Albiac, Jose L. Ansorena |
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| Přispěvatelé: | Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. INAMAT2 - Institute for Advanced Materials and Mathematics, Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila, Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. InaMat - Institute for Advanced Materials |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Sequence
Mathematics::Functional Analysis General Mathematics 010102 general mathematics Structure (category theory) Banach space Conditional bases 46B45 (Primary) 46B25 46B15 46B10 46B07 41A65 (Secondary) 01 natural sciences Functional Analysis (math.FA) Superreflexivity Conditionality constants Algebra Mathematics - Functional Analysis Besov spaces FOS: Mathematics Garling sequence spaces Christian ministry Almost greedy bases 0101 mathematics Subsymmetric basis Mathematics |
| Zdroj: | Academica-e: Repositorio Institucional de la Universidad Pública de Navarra Universidad Pública de Navarra Academica-e. Repositorio Institucional de la Universidad Pública de Navarra instname |
| Popis: | 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. 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. |
| Databáze: | OpenAIRE |
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