scholarly journals Dimension elevation in Müntz spaces: A new emergence of the Müntz condition

2014 ◽  
Vol 181 ◽  
pp. 6-17 ◽  
Author(s):  
Rachid Ait-Haddou
Keyword(s):  
Müntz Spaces ◽  
Dimension Elevation

Dimension elevation formula for Chebyshevian blossoms

2009 ◽  
Vol 26 (9) ◽  
pp. 1016-1027 ◽  
Author(s):  
Marie-Laurence Mazure
Keyword(s):  
Dimension Elevation

Embeddings of Müntz Spaces in

2019 ◽  
Vol 62 (1) ◽  
pp. 1-9
Author(s):  
Ihab Al Alam ◽  
Pascal Lefèvre
Keyword(s):  
Borel Measure ◽  
Essential Norm ◽  
Weak Compactness ◽  
Positive Borel Measure ◽  
Absolutely Continuous ◽  
Borel Measures ◽  
Embedding Operator ◽  
Müntz Spaces

AbstractIn this paper, we discuss the properties of the embedding operator $i_{\unicode[STIX]{x1D707}}^{\unicode[STIX]{x1D6EC}}:M_{\unicode[STIX]{x1D6EC}}^{\infty }{\hookrightarrow}L^{\infty }(\unicode[STIX]{x1D707})$, where $\unicode[STIX]{x1D707}$ is a positive Borel measure on $[0,1]$ and $M_{\unicode[STIX]{x1D6EC}}^{\infty }$ is a Müntz space. In particular, we compute the essential norm of this embedding. As a consequence, we recover some results of the first author. We also study the compactness (resp. weak compactness) and compute the essential norm (resp. generalized essential norm) of the embedding $i_{\unicode[STIX]{x1D707}_{1},\unicode[STIX]{x1D707}_{2}}:L^{\infty }(\unicode[STIX]{x1D707}_{1}){\hookrightarrow}L^{\infty }(\unicode[STIX]{x1D707}_{2})$, where $\unicode[STIX]{x1D707}_{1}$, $\unicode[STIX]{x1D707}_{2}$ are two positive Borel measures on [0, 1] with $\unicode[STIX]{x1D707}_{2}$ absolutely continuous with respect to $\unicode[STIX]{x1D707}_{1}$.

scholarly journals Lacunary Müntz spaces: isomorphisms and Carleson embeddings

2018 ◽  
Vol 68 (5) ◽  
pp. 2215-2251 ◽  
Author(s):  
Loïc Gaillard ◽  
Pascal Lefèvre
Keyword(s):  
Müntz Spaces

Dimension elevation is not always corner-cutting

2020 ◽  
Vol 109 ◽  
pp. 106529
Author(s):  
Carolina Vittoria Beccari ◽  
Giulio Casciola ◽  
Marie-Laurence Mazure
Keyword(s):  
Corner Cutting ◽  
Dimension Elevation

scholarly journals Two properties of Müntz spaces

2017 ◽  
Vol 50 (1) ◽  
pp. 239-244 ◽  
Author(s):  
Trond A. Abrahamsen ◽  
Aleksander Leraand ◽  
André Martiny ◽  
Olav Nygaard
Keyword(s):  
Dual Spaces ◽  
Müntz Spaces

Abstract We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.

scholarly journals Delta- and Daugavet points in Banach spaces

2020 ◽  
Vol 63 (2) ◽  
pp. 475-496
Author(s):  
T. A. Abrahamsen ◽  
R. Haller ◽  
V. Lima ◽  
K. Pirk
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Unit Ball ◽  
Banach Spaces ◽  
Unit Sphere ◽  
Closed Convex Hull ◽  
Müntz Spaces ◽  
Daugavet Property ◽  
Diameter Two Property

AbstractA Δ-point x of a Banach space is a norm-one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance 2 from x. If, in addition, every point in the unit ball is arbitrarily close to such convex combinations, x is a Daugavet point. A Banach space X has the Daugavet property if and only if every norm-one element is a Daugavet point. We show that Δ- and Daugavet points are the same in L1-spaces, in L1-preduals, as well as in a big class of Müntz spaces. We also provide an example of a Banach space where all points on the unit sphere are Δ-points, but none of them are Daugavet points. We also study the property that the unit ball is the closed convex hull of its Δ-points. This gives rise to a new diameter-two property that we call the convex diametral diameter-two property. We show that all C(K) spaces, K infinite compact Hausdorff, as well as all Müntz spaces have this property. Moreover, we show that this property is stable under absolute sums.

scholarly journals A Remez-Type Inequality for Non-dense Müntz Spaces with Explicit Bound

1998 ◽  
Vol 93 (3) ◽  
pp. 450-457 ◽  
Author(s):  
Peter Borwein ◽  
Tamás Erdélyi
Keyword(s):  
Type Inequality ◽  
Explicit Bound ◽  
Müntz Spaces

scholarly journals On the Geometry of Müntz Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Sergey V. Ludkovsky ◽  
Wolfgang Lusky
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces ◽  
Maximality Property ◽  
Müntz Spaces ◽  
Positive Integers

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].

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