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may 2020 Some Remarks on Schauder Bases in Lipschitz Free Spaces
Matěj Novotný
Bull. Belg. Math. Soc. Simon Stevin 27(1): 111-126 (may 2020). DOI: 10.36045/bbms/1590199307

Abstract

We show that the basis constant of every retractional Schauder basis on the Free space of a graph circle increases with the radius. As a consequence, there exists a uniformly discrete subset $M\subseteq\R^2$ such that $\F(M)$ does not have a retractional Schauder basis. Furthermore, we show that for any net $ N\subseteq\R^n$, $n\geq 2$, there is no retractional unconditional basis on the Free space $\mathcal F(N)$.

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Matěj Novotný. "Some Remarks on Schauder Bases in Lipschitz Free Spaces." Bull. Belg. Math. Soc. Simon Stevin 27 (1) 111 - 126, may 2020. https://doi.org/10.36045/bbms/1590199307

Information

Published: may 2020
First available in Project Euclid: 23 May 2020

zbMATH: 07213661
MathSciNet: MR4102704
Digital Object Identifier: 10.36045/bbms/1590199307

Subjects:
Primary: 46B03, 46B10

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 1 • may 2020
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