On the Riesz Almost Convergent Sequences Space
| Autor: | Mehmet Şengönül, Kuddusi Kayaduman |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2012 (2012) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2012/691694 |
| Popis: | 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∞. |
| Databáze: | Directory of Open Access Journals |
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