On the divergence of greedy algorithms with respect to Walsh subsystems in L

In this paper we prove that there exists a function f(x) which belongs to L1[0,1] such that a greedy algorithm with respect to the Walsh subsystem does not converge to f(x) in L1[0,1] norm, i.e. the Walsh subsystem {Wnk} is not a quasi-greedy basis in its linear span in L1.