Compact and Matrix Operators on the Space $\left\vert \overline N_p^{\phi }\right\vert _{k}$

Abstract

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from the space N φ p k , the space of all series summable by the absolute weighted mean summability method, to one of the classical sequence spaces c 0 , c, l ∞ . Also, we obtain the necessary and sufficient conditions for each matrix in these classes to be compact and establish a number of estimates or identities for the Hausdorff measures of noncompactness of the matrix operators in these classes.

Mutlak Cesa ́ro Seri Uzayı Ve Bazı Matris Dönüşümleri

“…In recent times, the literature has grown up concerned with characterizing all matrix operators which transform one given sequence space into another. For example, the absolute Ces𝑎𝑎́ro series space �𝐶𝐶 𝜆𝜆,𝜇𝜇 �(𝑝𝑝) has been introduced and some matrix characterizations of the matrix classes related to the space have been examined in , (see also (Gökçe, 2021;Gökçe and Sarıgöl, 2020;Gökçe and Sarıgöl, 2018;Gökçe and Sarıgöl, 2019a;Güleç, 2020;Sarıgöl, 2016;Zengin and İlkhan, 2019)). In this paper, we investigate the matrix class ��𝐶𝐶 𝜆𝜆,𝜇𝜇 �(𝑝𝑝), Γ� where Γ = {c, 𝑐𝑐 0 , 𝑙𝑙 ∞ }, and then we present some results.…”