[Banach] Abstract of a paper by Sergo A. Episkoposian

This is an announcement for the paper "On the divergence of greedy algorithms with respect to Walsh subsystems in $L$" by Sergo A. Episkoposian. Abstract: In this paper we prove that there exists a function which $f(x)$ belongs to $L^1[0,1]$ such that a greedy algorithm with regard to the Walsh subsystem does not converge to $f(x)$ in $L^1[0,1]$ norm, i.e. the Walsh subsystem $\{W_{n_k}\}$ is not a quasi-greedy basis in its linear span in $L^1$ Archive classification: math.FA Citation: Journal of Nonlinear Analysis Series A: Theory, Methods & The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1501.00832 or http://arXiv.org/abs/1501.00832