A remark on approximation with polynomials and greedy bases

Abstract

We investigate properties of the m-th error of approximation by polynomials with constant coefficients D m (x) and with modulus-constant coefficients D * m (x) introduced by Berná and Blasco (2016) to study greedy bases in Banach spaces. We characterize when lim inf m D m (x) and lim inf m D * m (x) are equivalent to x in terms of the democracy and superdemocracy functions, and provide sufficient conditions ensuring that lim m D * m (x) = lim m D m (x) = x , extending previous very particular results. 2000 Mathematics Subject Classification. 46B15, 41A65.