A Note On The Series Space |N ̅_p^θ |(μ)

Yıl 2019, Cilt: 23 Sayı: 4, 515 - 518, 01.08.2019

Fadime Gökçe

https://doi.org/10.16984/saufenbilder.486492

Öz

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  $l(\mu)$.

Anahtar Kelimeler

Absolute summability, Sequence spaces, Weighted mean, Duals, Isomorphism

Kaynakça

• [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.