Characterization of 1-quasi-greedy bases

• F. Albiac ^[1] ; J.L. Ansorena ^[2]
  1. [1] Universidad Pública de Navarra

     Universidad Pública de Navarra

     Pamplona, España

     
  2. [2] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 201, Nº 1 (January 2016), 2016, págs. 7-12
• Idioma: inglés
• DOI: 10.1016/j.jat.2015.08.006
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• Resumen

  • In this note we continue the study initiated in Albiac and Wojtaszczyk (2006) of greedy-like bases in the “isometric case”, i.e., in the case that the constants that arise in the context of greedy bases in their different forms are 1. Here we settle the problem to find a satisfactory characterization of 1-quasi-greedy bases in Banach spaces. We show that a semi-normalized basis in a Banach space is quasi-greedy with quasi-greedy constant 1 if and only if it is unconditional with suppression-unconditional constant 1.