Banach spaces with a unique greedy basis

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)80-102
Number of pages23
JournalJournal of Approximation Theory
StatePublished - Oct 1 2016


  • 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


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