The Cesaro-Gamma operator and its associated sequence space

摘要

In this paper, we introduce Cesaro-Gamma matrix that exhibits the structure of both the Cesaro and Gamma matrices. We study the domain of this new matrix in the space l(p) (1 <= p <= infinity). By this new matrix, we obtain a factorization for the infinite Hilbert matrix, based on the Cesaro matrix of order lambda, of the form H = (BC lambda)-C-lambda. As a second application of this operator, we obtain a factorization for the Cesaro matrix of order lambda of the form C lambda+(lambda) over tilde = (R lambda,(lambda) over tilde +1C(lambda) over tilde), which results in a factorization for the Cesaro matrices of the form C-lambda = (SC(lambda) over tilde)-C-lambda,(lambda) over tilde.