Geodesic
An Inclusion Theorem for Bohr-Hardy Summability Factors
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 653-658

Voir la notice de l'article provenant de la source Cambridge University Press

1. Let A denote a sequence to sequence transformation given by the normal matrix A = (ank )(n, k = 0, 1, 2, ...), i.e., a lower triangular matrix with ann ≠ 0 for all n. For B = (bnk ) we write B ⇒ A if every B limitable sequence is A limitable to the same limit, and say that B is equivalent to A if B ⇒ A and A ⇒ B. If B is normal, then it is well known that the inverse of B exists (we denote it by B -l) and that B ⇒ A if and only if F = AB -1 is a regular transformation, i.e., transforms every convergent sequence into a sequence converging to the same limit. We say that a series ∑ an † is summable A if its sequence of partial sums is A-limitable. 
Thorpe, B. An Inclusion Theorem for Bohr-Hardy Summability Factors. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 653-658. doi: 10.4153/CJM-1971-072-4
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