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

Norm of an operator T:X→Y is the best possible value of U satisfying the inequality ‖Tx‖Y≤U‖x‖X,and lower bound for T is the value of L satisfying the inequality ‖Tx‖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 ℓp(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 ℓp(w˜). [ABSTRACT FROM AUTHOR]