Embeddings and Lebesgue-Type Inequalities for the Greedy Algorithm in Banach Spaces

Pablo M. Berná, Oscar Blasco, Gustavo Garrigós, Eugenio Hernández, Timur Oikhberg

Research output: Contribution to journalArticlepeer-review


We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of not necessarily quasi-greedy bases.

Original languageEnglish (US)
Pages (from-to)415-451
Number of pages37
JournalConstructive Approximation
Issue number3
StatePublished - Dec 1 2018


  • Biorthogonal system
  • Discrete Lorentz space
  • Greedy algorithm
  • Lebesgue-type inequality
  • Non-linear approximation
  • Quasi-greedy basis

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


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