Tauberian conditions for Conull spaces
The typical Tauberian theorem asserts that a particular summability method cannot map any divergent member of a given set of sequences into a convergent sequence. These sets of sequences are typically defined by an order growth or gap condition. We establish that any conull space contains a bounded...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128500076X |
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| _version_ | 1832554453157281792 |
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| author | J. Connor A. K. Snyder |
| author_facet | J. Connor A. K. Snyder |
| author_sort | J. Connor |
| collection | DOAJ |
| description | The typical Tauberian theorem asserts that a particular summability method
cannot map any divergent member of a given set of sequences into a convergent sequence. These sets of sequences are typically defined by an order growth or gap condition. We establish that any conull space contains a bounded divergent member of such a set;
hence, such sets fail to generate Tauberian theorems for conull spaces. |
| format | Article |
| id | doaj-art-c3f2f13350bc4c2784688f98ded5de15 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c3f2f13350bc4c2784688f98ded5de152025-02-03T05:51:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018468969210.1155/S016117128500076XTauberian conditions for Conull spacesJ. Connor0A. K. Snyder1Department of Mathematical Sciences, Kent State University, Kent 44242, Ohio, USADepartment of Mathematics, Lehigh University, Bethlehem 18015, PA, USAThe typical Tauberian theorem asserts that a particular summability method cannot map any divergent member of a given set of sequences into a convergent sequence. These sets of sequences are typically defined by an order growth or gap condition. We establish that any conull space contains a bounded divergent member of such a set; hence, such sets fail to generate Tauberian theorems for conull spaces.http://dx.doi.org/10.1155/S016117128500076XFK space; conull. |
| spellingShingle | J. Connor A. K. Snyder Tauberian conditions for Conull spaces International Journal of Mathematics and Mathematical Sciences FK space; conull. |
| title | Tauberian conditions for Conull spaces |
| title_full | Tauberian conditions for Conull spaces |
| title_fullStr | Tauberian conditions for Conull spaces |
| title_full_unstemmed | Tauberian conditions for Conull spaces |
| title_short | Tauberian conditions for Conull spaces |
| title_sort | tauberian conditions for conull spaces |
| topic | FK space; conull. |
| url | http://dx.doi.org/10.1155/S016117128500076X |
| work_keys_str_mv | AT jconnor tauberianconditionsforconullspaces AT aksnyder tauberianconditionsforconullspaces |