Abstract In this study, novel sequence spaces are introduced as the domains of the Jordan-type matrix operator within the spaces of c and c₀ c 0. Initially, these new spaces are defined, and their fundamental properties, including completeness and other topological characteristics, are examined. Furthermore, the existence of a Schauder basis for these spaces is established, highlighting its crucial role in their structural analysis. Next, the α -, β -, and γ -duals of the newly constructed sequence spaces are determined to provide a deeper understanding of their duality relations. Subsequently, the classes of infinite matrices that map sequences from these new spaces into classical sequence spaces, such as ₚ ℓ p, ℓ ∞, c, and c₀ c 0, are characterized, along with the reverse transformations. Finally, attention is given to compact operators acting on these spaces, and a comprehensive characterization of their behavior is provided. Necessary and sufficient conditions for compactness are explored, and their implications in functional analysis are discussed.
Ellidokuzoğlu et al. (Sat,) studied this question.