Abstract and Applied Analysis
Volume 2009 (2009), Article ID 865371, 7 pages
Research Article

On Perfectly Homogeneous Bases in Quasi-Banach Spaces

Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain

Received 22 April 2009; Accepted 3 June 2009

Academic Editor: Simeon Reich

Copyright © 2009 F. Albiac and C. Leránoz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For 0<p< the unit vector basis of p has the property of perfect homogeneity: it is equivalent to all its normalized block basic sequences, that is, perfectly homogeneous bases are a special case of symmetric bases. For Banach spaces, a classical result of Zippin (1966) proved that perfectly homogeneous bases are equivalent to either the canonical c0-basis or the canonical p-basis for some 1p<. In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of p for 0<p<1 as well amongst bases in nonlocally convex quasi-Banach spaces.