Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases

Fernando Albiac; José Luis Ansorena; Stephen J. Dilworth; Denka Kutzarova

doi:10.4064/sm180910-1-2

Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases

Fernando Albiac, José Luis Ansorena, Stephen J. Dilworth, Denka Kutzarova

Mathematics

Research output: Contribution to journal › Article

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.

Original language	English (US)
Pages (from-to)	277-288
Number of pages	12
Journal	Studia Mathematica
Volume	251
Issue number	3
DOIs	https://doi.org/10.4064/sm180910-1-2
State	Published - 2020

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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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AU - Albiac, Fernando

AU - Ansorena, José Luis

AU - Dilworth, Stephen J.

AU - Kutzarova, Denka

PY - 2020

Y1 - 2020

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AB - 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.

U2 - 10.4064/sm180910-1-2

DO - 10.4064/sm180910-1-2

M3 - Article

VL - 251

SP - 277

EP - 288

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 3

ER -