Some Remarks on Schauder Bases in Lipschitz Free Spaces
Copyright policy )Some Remarks on Schauder Bases in Lipschitz Free Spaces
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 $M\subset\mathbb{R}^2$ such that $\mathcal F(M)$ does not have a retractional Schauder basis. Furthermore, we show that for any net $ N\subseteq\mathbb{R}^n$ there is no retractional unconditional basis on the Free space $\mathcal F(N)$.
Mathematics - Functional Analysis, 46B10, Isomorphic theory (including renorming) of Banach spaces, Schauder basis, extension operator, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, Lipschitz-free space, unconditionality, 46B03, Functional Analysis (math.FA)
Mathematics - Functional Analysis, 46B10, Isomorphic theory (including renorming) of Banach spaces, Schauder basis, extension operator, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, Lipschitz-free space, unconditionality, 46B03, Functional Analysis (math.FA)
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