On the Geometry of Müntz Spaces. (16th June 2015)

• Record Type: Journal Article
• Authors: Ludkovsky, Sergey V.; Lusky, Wolfgang
• Other Names: Hencl Stanislav Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-06-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/787291
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : LetΛ = { λ k } k = 1 ∞ satisfy0 < λ 1 < λ 2 < ⋯, ∑ k = 1 ∞ ‍ 1 / λ k < ∞ andi n f k ( λ k + 1 - λ k ) > 0 . We investigate the Müntz spacesM p Λ = s p a n ¯ { t λ k : k = 1, 2, … } ⊂ L p ( 0, 1 ) for1 ≤ p ≤ ∞ . We show that, for eachp, there is a Müntz spaceF p which contains isomorphic copies of all Müntz spaces as complemented subspaces.F p is uniquely determined up to isomorphisms by this maximality property. We discuss explicit descriptions ofF p . In particularF p is isomorphic to a Müntz spaceM p ( Λ ^ ) whereΛ ^ consists of positive integers. Finally we show that the Banach spaces( ∑ n ‍ ⊕ F n ) p for1 ≤ p < ∞ and( ∑ n ‍ ⊕ F n ) 0 forp = ∞ are always isomorphic to suitable Müntz spacesM p ( Λ ) if theF n are the spans of arbitrary finitely many monomials over[ 0, 1 ] .