Abstract and Applied Analysis

On Perfectly Homogeneous Bases in Quasi-Banach Spaces

F. Albiac and C. Leránoz

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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 c 0 -basis or the canonical p -basis for some 1 p < . 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.

Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 865371, 7 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745577

Digital Object Identifier
doi:10.1155/2009/865371

Mathematical Reviews number (MathSciNet)
MR2521126

Zentralblatt MATH identifier
1184.46003

Citation

Albiac, F.; Leránoz, C. On Perfectly Homogeneous Bases in Quasi-Banach Spaces. Abstr. Appl. Anal. 2009 (2009), Article ID 865371, 7 pages. doi:10.1155/2009/865371. https://projecteuclid.org/euclid.aaa/1268745577


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