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2009 On Perfectly Homogeneous Bases in Quasi-Banach Spaces
F. Albiac, C. Leránoz
Abstr. Appl. Anal. 2009: 1-7 (2009). DOI: 10.1155/2009/865371

Abstract

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.

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F. Albiac. C. Leránoz. "On Perfectly Homogeneous Bases in Quasi-Banach Spaces." Abstr. Appl. Anal. 2009 1 - 7, 2009. https://doi.org/10.1155/2009/865371

Information

Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1184.46003
MathSciNet: MR2521126
Digital Object Identifier: 10.1155/2009/865371

Rights: Copyright © 2009 Hindawi

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