A NEW BANACH SPACE DEFINED BY ABSOLUTE JORDAN TOTIENT MEANS

Abstract

In the present study, we have constructed a new Banach series space |Upsilon (R)|(u)(p) by using concept of absolute Jordan totient summability |Upsilon (R),u(n)|(p) which is derived by the infinite regular matrix of the Jordan's totient function. Also, we prove that the series space |Upsilon (R)|(u)(p) is linearly isomorphic to the space of all p-absolutely summable sequences & ell;(p) for p >= 1. Moreover, we compute the alpha-,beta- and gamma- duals of this space and construct Schauder basis for the series space |Upsilon (R)|(u)(p). Finally, we characterize the classes of infinite matrices (|Upsilon (R)|(u)(p),X) and (X,|Upsilon (R)|(u)(p)), where X is any given classical sequence spaces & ell;(infinity), c, c(0) and & ell;(1).