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Compact operators on the Motzkin sequence space c0(M)
(2024) ERDEM, Sezer
The concept of non-compactness measure is extremely beneficial for func- tional analysis in theories, such as fixed point and operator equations. Apart from these, the Hausdorff measure of non-compactness also has some applications in the theory of sequence spaces which is an interesting topic of functional analysis. One of these applications is to ob- tain necessary and sufficient conditions for the matrix operators between Banach coordinate (BK) spaces to be compact. In line with these explanations, in this study, the necessary and sufficient conditions for a matrix operator to be compact from the Motzkin sequence space c0(M) to the sequence space ? ? {??, c, c0, ?1} are presented by using Hausdorff measure of non-compactness.
On the $q$-Cesaro bounded double sequence space
(2024) ERDEM, Sezer
In this article, the new sequence space $\\tilde{\\mathcal{M}}_u^q$ is acquainted, described as the domain of the 4d (4-dimensional) $q$-Cesaro matrix operator, which is the $q$-analogue of the first order 4d Cesaro matrix operator, on the space of bounded double sequences. In the continuation of the study, the completeness of the new space is given, and the inclusion relation related to the space is presented. In the last two parts, the duals of the space are determined, and some matrix classes are acquired.