## Abstract and Applied Analysis

### On Perfectly Homogeneous Bases in Quasi-Banach Spaces

#### Abstract

For $0 \lt p \lt \infty$ the unit vector basis of ${\ell }_{p}$ 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 ${\ell }_{p}$-basis for some $1\leq p \lt \infty$. In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of ${\ell }_{p}$ for $0 \lt p \lt1$ 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

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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