Some new Cesàro sequence spaces of order \(\alpha \). (English) Zbl 07916742
Ukr. Math. J. 76, No. 3, 484-500 (2024) and Ukr. Mat. Zh. 76, No. 3, 432-446 (2024).
Summary: We introduce the spaces \(\ell_\infty(\mathcal{C}_\alpha )\), \(f ( \mathcal{C}_\alpha )\), and \(f_0( \mathcal{C}_\alpha )\) of Cesàro bounded, Cesàro almost convergent, and Cesàro almost null sequences of order \(\alpha ,\) respectively. Moreover, we establish some inclusion relations for these spaces and determine the \(\alpha\)-, \(\beta\)- and \(\gamma \)-duals of the spaces \(\ell_\infty (\mathcal{C}_\alpha )\) and \(f ( \mathcal{C}_\alpha ).\) Finally, we characterize the classes of matrix transformations from the space \(f ( \mathcal{C}_\alpha )\) to any sequence space \(Y\) and from any sequence space \(Y\) to the space \(f ( \mathcal{C}_\alpha ).\)
MSC:
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 40C05 | Matrix methods for summability |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
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