On the Pelczynski conjecture on Auerbach Bases
Functional Analysis
2016-10-19 v2 Algebraic Topology
Abstract
We consider Auerbach bases in Banach spaces of dimension n>2. We show that there exists at least (n-1)n/2+1 such bases. This estimate follows from the calculation of the Lusternik-Schnirelmann category of the flag variety. A better estimate is obtained for generic Banach spaces by the Morse theory.
Keywords
Cite
@article{arxiv.1608.00495,
title = {On the Pelczynski conjecture on Auerbach Bases},
author = {Andrzej Weber and Michał Wojciechowski},
journal= {arXiv preprint arXiv:1608.00495},
year = {2016}
}