On Perfectly Homogeneous Bases in Quasi-Banach Spaces
Keyword(s):
For0<p<∞the unit vector basis ofℓphas 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 canonicalc0-basis or the canonicalℓp-basis for some1≤p<∞. In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases ofℓpfor0<p<1as well amongst bases in nonlocally convex quasi-Banach spaces.
1975 ◽
Vol 18
(1)
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pp. 137-140
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1975 ◽
Vol 20
(3-4)
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pp. 216-227
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1996 ◽
Vol 48
(3)
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pp. 625-640
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1986 ◽
Vol 29
(3)
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pp. 329-333
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2007 ◽
Vol 75
(2)
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pp. 193-210
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