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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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000690 |
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| _version_ | 1850212093671768064 |
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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. |
| format | Article |
| id | doaj-art-8b3f54c34cbf4fdaa4e85772ecfec5f1 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |