On the Geometry of Müntz Spaces
Keyword(s):
LetΛ={λk}k=1∞satisfy0<λ1<λ2<⋯,∑k=1∞1/λk<∞andinfk(λk+1-λk)>0. We investigate the Müntz spacesMpΛ=span¯{tλk:k=1,2,…}⊂Lp(0,1)for1≤p≤∞. We show that, for eachp, there is a Müntz spaceFpwhich contains isomorphic copies of all Müntz spaces as complemented subspaces.Fpis uniquely determined up to isomorphisms by this maximality property. We discuss explicit descriptions ofFp. In particularFpis isomorphic to a Müntz spaceMp(Λ^)whereΛ^consists of positive integers. Finally we show that the Banach spaces(∑n⊕Fn)pfor1≤p<∞and(∑n⊕Fn)0forp=∞are always isomorphic to suitable Müntz spacesMp(Λ)if theFnare the spans of arbitrary finitely many monomials over[0,1].
1996 ◽
Vol 124
(7)
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pp. 2005-2012
2019 ◽
Vol 4
(2)
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pp. 369-387
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2017 ◽
Vol 38
(11)
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pp. 1490-1506
1995 ◽
Vol 18
(3)
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pp. 437-442
1988 ◽
Vol 153
(1)
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pp. 175-190
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2020 ◽
Vol 63
(2)
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pp. 475-496
Keyword(s):
1989 ◽
Vol 316
(1)
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pp. 215
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