On a class of linear operators on ℓp and its schur multipliers

In this paper we consider the spaces Bw(ℓp), 1 ≤ p ≤ ∞, of infinite matrices A defined by (Equation presented) and prove that Bw(ℓp) is not closed under this product. Moreover, we prove that linear and bounded operators on ℓp are Schur multipliers on Bw(ℓp), a result which is not obvious, since Bw(ℓp) is not a Schur algebra. Most of the results are sharp in the sense that they are given via necessary and sufficient conditions.Validerad; 2016; Nivå 2; 20160510 (andbra)