Renorming spaces with greedy bases

S. J. Dilworth, D. Kutzarova, E. Odell, Th Schlumprecht, A. Zsák

Research output: Contribution to journalArticlepeer-review


We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given ε>0, so that the basis becomes (1+ε)-democratic, and hence (2+ε)-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is (1+ε)-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in Lp[0, 1], 1<p<∞, and in dyadic Hardy space H1, as well as the unit vector basis of Tsirelson space.

Original languageEnglish (US)
Pages (from-to)39-56
Number of pages18
JournalJournal of Approximation Theory
StatePublished - Dec 1 2014


  • Democratic basis
  • Fundamental function
  • Greedy basis
  • M-term approximation
  • Renorming

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • General Mathematics
  • Applied Mathematics


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