On Perfectly Homogeneous Bases in Quasi-Banach SpacesReport as inadecuate




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Abstract and Applied AnalysisVolume 2009 2009, Article ID 865371, 7 pages

Research ArticleDepartamento 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.

Abstract

For the unit vector basis of has the property of perfect homogeneity: it is equivalent to all its normalized block basicsequences, that is, perfectly homogeneous bases are a special case ofsymmetric bases. For Banach spaces, a classical result of Zippin 1966proved that perfectly homogeneous bases are equivalent to either thecanonical -basis or the canonical -basis for some . In this note, we show that a relaxed form of perfect homogeneity characterizesthe unit vector bases of for as well amongst bases in nonlocally convex quasi-Banach spaces.





Author: F. Albiac and C. Leránoz

Source: https://www.hindawi.com/



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