The bounds for matrices with monotonic rows

Abstract

The bounds L X,Y (A) and A X,Y of an operator A = (a n,k ) n, k≥0 with monotonic rows are evaluated, where X and Y are quasi-normed real valued sequence spaces. In particular, in the case where X = p and Y = q , our results give the results when part 0 < p ≤ 1 and 0 < q < ∞ to complement the other results with range p ≥ 1 and 0 < q < ∞. Moreover, we give a partial answer to a problem [1, Problem 7.23] which was posed by Bennett.