On the Riesz Almost Convergent Sequences Space
The purpose of this paper is to introduce new spaces 𝑓 and 𝑓0 that consist of all sequences whose Riesz transforms of order one are in the spaces 𝑓 and 𝑓0, respectively. We also show that 𝑓 and 𝑓0 are linearly isomorphic to the spaces 𝑓 and 𝑓0, respectively. The 𝛽- and 𝛾-duals of the spaces 𝑓 a...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/691694 |
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| author | Mehmet Şengönül Kuddusi Kayaduman |
| author_facet | Mehmet Şengönül Kuddusi Kayaduman |
| author_sort | Mehmet Şengönül |
| collection | DOAJ |
| description | The purpose of this paper is to introduce new spaces 𝑓 and 𝑓0 that consist of all sequences whose Riesz transforms of order one are in the spaces 𝑓 and 𝑓0, respectively. We also show that 𝑓 and 𝑓0 are linearly isomorphic to the spaces 𝑓 and 𝑓0, respectively. The 𝛽- and 𝛾-duals of the spaces 𝑓 and 𝑓0 are computed. Furthermore, the classes (𝑓∶𝜇) and (𝜇∶𝑓) of infinite matrices are characterized for any given sequence space 𝜇 and determine the necessary and sufficient conditions on a matrix 𝐴 to satisfy 𝐵𝑅−core(𝐴𝑥)⊆𝐾−core(𝑥), 𝐵𝑅−core(𝐴𝑥)⊆𝑠𝑡−core(𝑥) for all 𝑥∈ℓ∞. |
| format | Article |
| id | doaj-art-d7228b2d787e4545a99000427ec683cd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d7228b2d787e4545a99000427ec683cd2025-02-03T07:24:20ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/691694691694On the Riesz Almost Convergent Sequences SpaceMehmet Şengönül0Kuddusi Kayaduman1Faculty of Science and Letters, Nevşehir University, 50300 Nevşehir, TurkeyFaculty of Arts and Sciences, University of Gaziantep, 27310 Gaziantep, TurkeyThe purpose of this paper is to introduce new spaces 𝑓 and 𝑓0 that consist of all sequences whose Riesz transforms of order one are in the spaces 𝑓 and 𝑓0, respectively. We also show that 𝑓 and 𝑓0 are linearly isomorphic to the spaces 𝑓 and 𝑓0, respectively. The 𝛽- and 𝛾-duals of the spaces 𝑓 and 𝑓0 are computed. Furthermore, the classes (𝑓∶𝜇) and (𝜇∶𝑓) of infinite matrices are characterized for any given sequence space 𝜇 and determine the necessary and sufficient conditions on a matrix 𝐴 to satisfy 𝐵𝑅−core(𝐴𝑥)⊆𝐾−core(𝑥), 𝐵𝑅−core(𝐴𝑥)⊆𝑠𝑡−core(𝑥) for all 𝑥∈ℓ∞.http://dx.doi.org/10.1155/2012/691694 |
| spellingShingle | Mehmet Şengönül Kuddusi Kayaduman On the Riesz Almost Convergent Sequences Space Abstract and Applied Analysis |
| title | On the Riesz Almost Convergent Sequences Space |
| title_full | On the Riesz Almost Convergent Sequences Space |
| title_fullStr | On the Riesz Almost Convergent Sequences Space |
| title_full_unstemmed | On the Riesz Almost Convergent Sequences Space |
| title_short | On the Riesz Almost Convergent Sequences Space |
| title_sort | on the riesz almost convergent sequences space |
| url | http://dx.doi.org/10.1155/2012/691694 |
| work_keys_str_mv | AT mehmetsengonul ontherieszalmostconvergentsequencesspace AT kuddusikayaduman ontherieszalmostconvergentsequencesspace |