On Perfectly Homogeneous Bases in Quasi-Banach Spaces
For 0<p<∞ the unit vector basis of ℓp 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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/865371 |
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| Summary: | For 0<p<∞ the unit vector basis of ℓp 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 ℓp-basis for some 1≤p<∞. In this note, we show that (a relaxed form of) perfect homogeneity characterizes
the unit vector bases of ℓp for 0<p<1 as well amongst bases in nonlocally convex quasi-Banach spaces. |
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| ISSN: | 1085-3375 1687-0409 |