Some Remarks on Schauder Bases in Lipschitz Free Spaces

Result of project: Cluster 4.0 – Methodology of System Integration
ID project: EF16_026/0008432
Author: Novotný, M.
Published in: The Belgian Mathematical Society (May 2020), BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN (Volume: 27, Issue: 1, Pages: 111-126)
DOI: 10.36045/bbms/1590199307


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 _ R2 such that F(M) does not have a retractional Schauder basis. Furthermore, we show that for any net N _ Rn, n _ 2, there is no retractional unconditional basis on the Free space F(N).

This project has received funding from the Ministry of Education, Youth and Sports, program Operational Programme Research, Development and Education under agreement No. EF16_026/0008432.