Some New Cauchy Sequence Spaces

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Universal Journal of Mathematics and Applications
Volume:1 Issue:4
Some New Cauchy Sequence Spaces

Some New Cauchy Sequence Spaces

Pages : 267-272

View : 85 | Download : 7

Publication Date : 2018-12-20

Article Type : Research Paper

Abstract :In this paper, our goal is to introduce some new Cauchy sequence spaces. These spaces are defined by Cauchy transforms. We shall use notations $C_{\infty }\leftinsert ignore into journalissuearticles values( s,t\right); $, $C\leftinsert ignore into journalissuearticles values( s,t\right); $ and $C_{0}\leftinsert ignore into journalissuearticles values( s,t\right); ~$for these new sequence spaces. We prove that these new sequence spaces $C_{\infty }\leftinsert ignore into journalissuearticles values( s,t\right); $, $C\leftinsert ignore into journalissuearticles values( s,t\right); $ and $C_{0}\leftinsert ignore into journalissuearticles values( s,t\right); ~$ are the $BK-$spaces and isomorphic to the spaces $l_{\infty }$, $c\ $and $c_{0}$, respectively. Besides the bases of these spaces, $\alpha -$, $\beta -\ $and $\gamma -$ duals of these spaces will be given. Finally, the matrix classes $insert ignore into journalissuearticles values(C\leftinsert ignore into journalissuearticles values( s,t\right); :l_{p});$ and $insert ignore into journalissuearticles values(C\leftinsert ignore into journalissuearticles values( s,t\right); :c);$ have been characterized.
Keywords : Cauchy sequence spaces, alpha, eta and gamma duals, Schauder basis, Matrix mappings

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