Renorming spaces with greedy bases Academic Article uri icon


  • 2014 Elsevier Inc. 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 >0, so that the basis becomes (1+)-democratic, and hence (2+)-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+)-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

published proceedings

  • Journal of Approximation Theory

author list (cited authors)

  • Dilworth, S. J., Kutzarova, D., Odell, E., Schlumprecht, T. h., & Zsk, A.

citation count

  • 13

complete list of authors

  • Dilworth, SJ||Kutzarova, D||Odell, E||Schlumprecht, Th||Zsák, A

publication date

  • January 2014