Some Sequence Spaces Using Leonardo Numbers

In this paper, we introduce and analyze a new class of sequence spaces generated through a matrix constructed from Leonardo numbers (Len). Specifically, we define a matrix Q=(Q˜nk) by Q˜nk={LekLen+2−(n+3),1≤k≤n,0,k>n,and employ it to develop the matrix-domain sequence spaces lp(Q), l∞(Q), c(Q), and c0(Q). We carry out a comprehensive investigation of their topological and structural properties, including completeness, BK-space structure, solidity, inclusion relations, norm isomorphisms with classical sequence spaces, and the existence of Schauder bases. The geometric features of these spaces are also examined, especially, approximation property, the Radon–Riesz property, the Hahn–Banach extension property and rotundity. Furthermore, we determine the α-, β-, and γ-duals of the newly introduced spaces. In addition, we characterize matrix transformations not only of the form (X(Q),Y) but also of the more general classes (X(Q),Y(Q)), where X,Y∈{lp,l∞,c,c0}. We establish necessary and sufficient conditions for infinite matrices to map between these matrix-domain spaces.