The Abel-type transformations into ℓ

Mulatu Lemma

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-10

Abstract:

Let t be a sequence in ( 0 , 1 ) that converges to 1 , and define the Abel-type matrix A α , t by a n k = ( k + α k ) t n k + 1 ( 1 − t n ) α + 1 for α > − 1 . The matrix A α , t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings into ℓ . Necessary and sufficient conditions for A α , t to be ℓ - ℓ , G - ℓ , and G w - ℓ are established. Also, the strength of A α , t in the ℓ - ℓ setting is investigated.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:108958

DOI: 10.1155/S0161171299227755

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