On the Geometry of Müntz Spaces
Joint Authors
Ludkovsky, Sergey V.
Lusky, Wolfgang
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-06-16
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Let Λ = { λ k } k = 1 ∞ satisfy 0 < λ 1 < λ 2 < ⋯ , ∑ k = 1 ∞ 1 / λ k < ∞ and i n f k ( λ k + 1 - λ k ) > 0 .
We investigate the Müntz spaces M p Λ = s p a n ¯ { t λ k : k = 1,2 , … } ⊂ L p ( 0,1 ) for 1 ≤ p ≤ ∞ .
We show that, for each p , there is a Müntz space F 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 of F p .
In particular F p is isomorphic to a Müntz space M p ( Λ ^ ) where Λ ^ consists of positive integers.
Finally we show that the Banach spaces ( ∑ n ⊕ F n ) p for 1 ≤ p < ∞ and ( ∑ n ⊕ F n ) 0 for p = ∞ are always isomorphic to suitable Müntz spaces M p ( Λ ) if the F n are the spans of arbitrary finitely many monomials over [ 0,1 ] .
American Psychological Association (APA)
Ludkovsky, Sergey V.& Lusky, Wolfgang. 2015. On the Geometry of Müntz Spaces. Journal of Function Spaces،Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1068323
Modern Language Association (MLA)
Ludkovsky, Sergey V.& Lusky, Wolfgang. On the Geometry of Müntz Spaces. Journal of Function Spaces No. 2015 (2015), pp.1-7.
https://search.emarefa.net/detail/BIM-1068323
American Medical Association (AMA)
Ludkovsky, Sergey V.& Lusky, Wolfgang. On the Geometry of Müntz Spaces. Journal of Function Spaces. 2015. Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1068323
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068323