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    APPLICATION OF JORDAN-TYPE MATRIX OPERATOR IN THE THEORY OF SEQUENCE SPACES
    (Palestine Polytechnic University, 2026) Erdem, S.; Ellidokuzoğlu, H.B.; Demiriz, S.; Kara, M.İ.
    This research introduces a novel regular matrix operator uniquely characterized by an arithmetic Jordan-type function. The study primarily investigates its domains in the sequence spaces of absolutely p-summable and bounded sequences, establishing the theoretical framework supporting these analyses. It further explores fundamental properties, inclusion relations, and the Schauder basis of these spaces, providing insights into their topological and functional structure. The identification of α-, β-and γ-duals enhances the theoretical contributions by offering a dual perspective on the studied spaces. Additionally, the classification of certain matrix classes aids in characterizing the operator’s action across different mathematical settings. Finally, a detailed examination of a specific class of compact operators acting on the newly introduced sequence spaces highlights their significance and applicability. © Palestine Polytechnic University-PPU 2026.
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