On Perfectly Homogeneous Bases in Quasi-Banach Spaces

F. Albiac and C. Leránoz

Abstract and Applied Analysis, 2009, vol. 2009, 1-7

Abstract:

For the unit vector basis of 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 -basis or the canonical -basis for some . In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of for as well amongst bases in nonlocally convex quasi-Banach spaces.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:865371

DOI: 10.1155/2009/865371

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