The two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on $l_p$. The theorems are applied to N\"orlund and weighted mean matrices.

Keywords:

Triangular matrices, Nörlund matrices, weighted means, operators, on $l_p$. Triangular matrices, Nörlund matrices, weighted means, operators, on $l_p$.

MSC Classifications:

47B37, 47A30, 40G05 show english descriptions Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Norms (inequalities, more than one norm, etc.)
Cesaro, Euler, Norlund and Hausdorff methods 47B37 - Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A30 - Norms (inequalities, more than one norm, etc.)
40G05 - Cesaro, Euler, Norlund and Hausdorff methods

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