Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

摘要

> Norm of an operator T : X → Y is the best possible value of U satisfying the inequality ‖ T x ‖ Y ≤ U ‖ x ‖ X , and lower bound for T is the value of L satisfying the inequality ‖ T x ‖ Y ≥ L ‖ x ‖ X , where ‖.‖ _X and ‖.‖ _Y are the norms on the spaces X and Y , respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space ? _p ( w ) into a new space called as Fibonacci weighted difference sequence space. For this purpose, we firstly introduce the Fibonacci difference matrix F ? and the space consisting of sequences whose F ? ‐transforms are in ? p (