Banach spaces with a unique greedy basis

F. Albiac; J. L. Ansorena; S. J. Dilworth; Denka Kutzarova

doi:10.1016/j.jat.2016.06.005

Banach spaces with a unique greedy basis

F. Albiac, J. L. Ansorena, S. J. Dilworth, Denka Kutzarova

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c₀, ℓ₁, and ℓ₂) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected.

Original language	English (US)
Pages (from-to)	80-102
Number of pages	23
Journal	Journal of Approximation Theory
Volume	210
DOIs	https://doi.org/10.1016/j.jat.2016.06.005
State	Published - Oct 1 2016

Keywords

Greedy basis
Marcinkiewicz spaces
Nakano spaces
Orlicz sequence spaces
Symmetric basis
Unconditional basis
Uniqueness greedy (respectively, unconditional or symmetric) basis

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

Online availability

10.1016/j.jat.2016.06.005

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abstract = "The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c0, ℓ1, and ℓ2) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected.",

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AU - Albiac, F.

AU - Ansorena, J. L.

AU - Dilworth, S. J.

AU - Kutzarova, Denka

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AB - The purpose of this article is to undertake an in-depth study of the properties of existence and uniqueness of greedy bases in Banach spaces. We show that greedy bases fail to exist for a range of neo-classical spaces within the family of Nakano and Orlicz sequence spaces and find the first-known cases of non-trivial spaces (i.e., different from c0, ℓ1, and ℓ2) with a unique greedy basis. The variety and nature of those examples evince that a complete classification of Banach spaces with a unique greedy basis cannot be expected.

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KW - Marcinkiewicz spaces

KW - Nakano spaces

KW - Orlicz sequence spaces

KW - Symmetric basis

KW - Unconditional basis

KW - Uniqueness greedy (respectively, unconditional or symmetric) basis

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Banach spaces with a unique greedy basis

Abstract

Keywords

ASJC Scopus subject areas

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