Nörlund Operators On lp

Abstract

AbstractThe Nörlund matrix Na is the triangular matrix {an-k /An}, where an ≥ 0 and An := a0 + a1 + • • • + an > 0. It is proved that, subject to the existence of α := lim nan/An, Na ∊ B(lp) for 1 < p < ∞ if and only if α < ∞. It is also proved that it is possible to have Na ∊ B(lp) for 1 < p < ∞ when sup nan/An = ∞.