On Absolute Cesa ́ro Series Space And Certain Matrix Transformations
Abstract
On recent paper, the paranormed space |C_(λ,μ) |(p) which is defined as the domain of Cesa ́ro matrix in the Maddox’s space l(p) has been introduced and studied in (Gökçe and Sarıgöl, 2019). In this study, some characterizations of matrix operators from the Absolute Cesa ́ro series space |C_(λ,μ) |(p) to the classical sequence spaces c,c_0,l_∞ are given. Also, it is shown that the matrix operators between the absolute Cesa ́ro series space and the spaces c,c_0,l_∞ are bounded operators. Finally, certain results are obtained as a special case.
Keywords
Absolute summability, matrix transformations, Cesa ́ro matrix, bounded linear operators
References
- Gökçe, F. (2021). Compact and Matrix Operators on the Space |N ̅_P^θ |_k. Fundamental Journal of Mathematics and Applications 4(2), 124-133.
- Gökçe, F., Sarıgöl, M.A. (2020). Series spaces derived from absolute Fibonacci summability and matrix transformations. Bollettino dell'Unione Matematica Italiana, 13, 29-38.
- Gökçe, F., Sarıgöl, M.A. (2019). Generalization of the absolute Ces`aro space and some matrix transformations. Numerical Functional Analysis and Optimization, 40, 1039-1052.
- Gökçe, F., Sarıgöl, M.A. (2019a). Extension of Maddox’s space l(μ) with Nörlund means. Asian-European Journal of Mathematics 12.06 (2019), 2040005.
- Gökçe, F., Sarıgöl, M.A. (2018). A new series space |N ̅_P^θ |(μ) and matrix transformations with applications. Kuwait Journal of Science, 45(4), 1-8.
- Grosse – Erdmann, K.G. (1993). Matrix transformations between the sequence spaces of Maddox, Journal of Mathematical Analysis and Applications, 180(1), 223-238.
- Güleç, G. C. H. (2020). Applications of measure of noncompactness in the series spaces of generalized absolute Cesaro means. Karadeniz Fen Bilimleri Dergisi, 10(1), 60-73.
- Maddox, I.J. (1969). Some properties of paranormed sequence spaces, Journal of the London Mathematical Society, 1, 316-322.
- Maddox, I.J. (1968). Paranormed sequence spaces generated by infinite matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 64, 335-340.
- Maddox, I.J. (1967). Spaces of strongly summable sequences, The Quarterly Journal of Mathematics 18, 345 -355
