Sequence spaces derived by the triple band generalized Fibonacci difference operator

[摘要] In this article we introduce the generalized Fibonacci difference operator$\mathsf{F}(\mathsf{B})$ by the composition of a Fibonacci band matrix F and a triple band matrix$\mathsf{B}(x,y,z)$ and study the spaces$\ell _{k}( \mathsf{F}(\mathsf{B}))$ and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ . We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces$\ell _{k}(\mathsf{F}(\mathsf{B}))$ and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ to space$\mathsf{Y}\in \{\ell _{\infty },c_{0},c,\ell _{1},cs_{0},cs,bs\}$ and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces$\ell _{k}(\mathsf{F}(\mathsf{B}))$ and$\ell _{\infty }(\mathsf{F}(\mathsf{B}))$ to$\mathsf{Y}\in \{ \ell _{\infty }, c, c_{0}, \ell _{1},cs_{0},cs,bs\} $ using the Hausdorff measure of non-compactness.

[学科分类] 航空航天科学

[关键词] Fibonacci difference space;Schauder basis;α -;β -;γ -duals;Matrix mappings;Compact operators;Hausdorff measure of non-compactness