We can describe the norm for an operator given as T:X→Y as follows: It is the most suitable value of U satisfying the following inequality ‖Tx‖_{Y}≤U‖x‖_{X} and also for the lower bound of T we can say that the value of L conforms to the following inequality ‖Tx‖_{Y}≥L‖x‖_{X}, where ‖.‖_{X} and ‖.‖_{Y} stand for the norms corresponding to the X and Y spaces, respectively. The most important characteristics of the present article lies in its computing the norms and lower bounds of those matrix operators used as weighted sequence space ℓ_{p}(w) upon a new one. This new sequence space is the generalized weighted sequence one. For this aim, the difference matrix B(r,s) and also the space consisting of those sequence whose B(r,s) transforms lie inside ℓ_{p}(w), in which r,s are taken from R.
2010 Mathematics Subject Classification. 46A45, 26D15, 40G05, 47B37.