General Summability Factor Theorems and Applications

We obtain sufficient and (different) necessary conditions for the series ∑ aₙ, which is absolutely summable of order k by a triangular matrix method A, to be such that ∑ aₙλₙ is absolutely summable of order k by a triangular matrix B. As corollaries we obtain a number of inclusion theorems. 2000 Mathematics Subject Classification. Primary: 40G99; Secondary: 40G05, 40D15