@article{1c33e1925c604414b6c4f1ce7485a06b,
title = "Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases",
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.",
keywords = "Almost greedy bases, Besov spaces, Conditional bases, Conditionality constants, Garling sequence spaces, Subsymmetric basis, Superreflexivity",
author = "Fernando Albiac and Ansorena, {Jos{\'e} Luis} and Dilworth, {Stephen J.} and Denka Kutzarova",
note = "Funding Information: Acknowledgements. 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 An{\'a}lisis Vectorial, multilineal, y aproxi-maci{\'o}n. 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. Dil-worth and D. Kutzarova were supported by the Workshop in Analysis and Probability at Texas A&M University in 2017.",
year = "2020",
doi = "10.4064/sm180910-1-2",
language = "English (US)",
volume = "251",
pages = "277--288",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",
number = "3",
}