New Matrix Domains Arising from the Euler Totient Function and Its Summatory Function

The matrix formed using the Euler totient function together with its summatory function is employed to generate new sequence spaces. After establishing several features of these spaces, their duals are explicitly identified. Subsequent sections provide the characterization of a number of matrix transformations acting on the new domains. The paper concludes with an investigation of the compactness of operators associated with the aforementioned matrix on the space of null sequences.