Some remarks on summability factors
If A, B are two summability methods, then (A,B) denotes the set of sequence \(\{\epsilon_ k\}\) such that \(\sum^{\infty}_{k=0}u_ k\epsilon_ k\) is summable B whenever \(\sum^{\infty}_{k=0}u_ k\) is summable A. If A is (C,\(\alpha)\), where \(\alpha\geq 0\), and if B is stronger than A then, although the set of B summable series is larger than the set of A summable series, the set (A,B) is the same as the set (A,A). This raises the question of whether this is a special property of the Cesàro methods, or whether a similar result holds for all regular summability methods. An example is given of a regular summability method for which such a result does not hold.
scientific article; zbMATH DE number 3939898