Noninclusion theorems for summability matrices

For both ordinary convergence and ℓ1-summability explicit sufficient conditions on a matrix have long been known that ensure that the summability method is strictly stronger than the identity map. The main results herein show that a matrix that satisfies those conditions can be included by another m...

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Main Author: J. A. Fridy
Format: Article
Language:English
Published: Wiley 1997-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171297000690
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author J. A. Fridy
author_facet J. A. Fridy
author_sort J. A. Fridy
collection DOAJ
description For both ordinary convergence and ℓ1-summability explicit sufficient conditions on a matrix have long been known that ensure that the summability method is strictly stronger than the identity map. The main results herein show that a matrix that satisfies those conditions can be included by another matrix only if the other matrix satisfies those same conditions.
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1687-0425
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publishDate 1997-01-01
publisher Wiley
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-8b3f54c34cbf4fdaa4e85772ecfec5f12025-08-20T02:09:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120351151610.1155/S0161171297000690Noninclusion theorems for summability matricesJ. A. Fridy0Department of Mathematics and Computer Science, Kent State University, Kent 44242, Ohio, USAFor both ordinary convergence and ℓ1-summability explicit sufficient conditions on a matrix have long been known that ensure that the summability method is strictly stronger than the identity map. The main results herein show that a matrix that satisfies those conditions can be included by another matrix only if the other matrix satisfies those same conditions.http://dx.doi.org/10.1155/S0161171297000690regular matrixℓ−ℓ matrix(summability) inclusionSilverman-Töeplitz conditionsKnopp-Lorentz conditions.
spellingShingle J. A. Fridy
Noninclusion theorems for summability matrices
International Journal of Mathematics and Mathematical Sciences
regular matrix
ℓ−ℓ matrix
(summability) inclusion
Silverman-Töeplitz conditions
Knopp-Lorentz conditions.
title Noninclusion theorems for summability matrices
title_full Noninclusion theorems for summability matrices
title_fullStr Noninclusion theorems for summability matrices
title_full_unstemmed Noninclusion theorems for summability matrices
title_short Noninclusion theorems for summability matrices
title_sort noninclusion theorems for summability matrices
topic regular matrix
ℓ−ℓ matrix
(summability) inclusion
Silverman-Töeplitz conditions
Knopp-Lorentz conditions.
url http://dx.doi.org/10.1155/S0161171297000690
work_keys_str_mv AT jafridy noninclusiontheoremsforsummabilitymatrices