A Note On The Series Space |N ̅_p^θ |(μ)
Abstract
The series space $\left\vert \bar{N}_{p}^{\theta }\right\vert\left( \mu \right) $ has recently been introduced and studied by Gökçe and Sarıgöl [1]. The main purpose of this paper is to determine the $\alpha-$, $\beta-$ and $\gamma$_duals of the space and to show that it is linearly isomorphic to the Maddox’s space $l(\mu)$.
Keywords
References
- [1] F. Gökçe and M.A. Sarıgöl, “A new series space |N ̅_p^θ |(μ) and matrix operatör with applications”, Kuwait Journal of Science, vol. 45, no. 4, pp. 1-8, 2018.[2] I.J.. Maddox,, “Some properties of paranormed sequence spaces,” Journal of the London Mathematical Society, vol. 1, pp. 316–322, 1969.[3] I.J.. Maddox, “Paranormed sequence spaces Generated by infinite matrices,”Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335–340, 1968.[4] I.J. Maddox, “Spaces of strongly summable sequences,” The Quarterly Journal of Mathematics, vol. 18, pp. 345–355, 1967.[5] H. Bor, “On |N ̅,p_n |_k summability factors of infinite series,” Tamkang J. Math, vol. 16, no. 1, pp. 13– 20, 1985.[6] T.M. FLett,, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proc. London Math. Soc., vol. 7, pp. 113-141, 1957.[7] M.A. Sarıgöl, “Spaces of series summable by absolute Cesàro and matrix operators,” Comm. Math. Appl., vol. 7, pp. 11–22, 2016.[8] M.A. Sarıgöl, “Norms and compactness of operators on absolute weighted mean, summable series,” Kuwait Journal of Science, vol. 43, no. 4, pp. 68–74, 2016.[9] M.A. Sarıgöl, “An inequality for matrix operators and its applications.,” J. Classical Anal, vol. 2, pp. 145–150, 2013. [10] M.A. Sarıgöl, “Matrix transformations on fields of absolute weighted mean summability,” Studia Scientiarum Mathematicarum Hungarica., vol. 48, no. 3, pp. 331–341, 2011.[11] M.A. Sarıgöl, “On local properties of factored Fourier series.,” Appl. Math. Comp., vol. 216, no. 3, pp. 3386–3390, 2010.[12] K.G. Grosse-Erdmann,, “Matrix transformations between the sequence spaces of Maddox.,” Journal of Mathematical Analysis and Applications, vol. 180, pp. 223–238, 1993.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Fadime Gökçe
*
0000-0003-1819-3317
Türkiye
Publication Date
August 1, 2019
Submission Date
November 21, 2018
Acceptance Date
December 11, 2018
Published in Issue
Year 2019 Volume: 23 Number: 4