Some attributes of the matrix operators about the weighted generalized difference sequence space

Authors : Murat CANDAN

Pages : 37-50

View : 68 | Download : 184

Publication Date : 2023-05-03

Article Type : Research Paper

Abstract :We can describe the norm for an operator given as T:X→Y as follows: It is the most appropriate value of U that satisfies the following inequality ‖Tx‖_{Y}≤U‖x‖_{X} and also for the lower bound of T we can say that the value of L agrees with the following inequality ‖Tx‖_{Y}≥L‖x‖_{X}, where ‖.‖_{X} and ‖.‖_{Y} stand for the norms corresponding to the spaces X and Y. The main feature of this article is that it converts the norms and lower bounds of those matrix operators used as weighted sequence space ℓ_{p}insert ignore into journalissuearticles values(w); into a new space. This new sequence space is the generalized weighted sequence space. For this purpose, the double sequential band matrix Binsert ignore into journalissuearticles values(r,s); and also the space consisting of those sequences whose Binsert ignore into journalissuearticles values(r,s); transforms lie inside ℓ_{p}insert ignore into journalissuearticles values(w);, where r=insert ignore into journalissuearticles values(r_{n});, s=insert ignore into journalissuearticles values(s_{n}); are convergent sequences of positive real numbers. When comparing with the corresponding results in the literature, it can be seen that the results of the present study are more general and comprehensive.
Keywords : Sequence spaces, matrix operators, quasi summable matrices

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