The Cesàro–Gamma operator and its associated sequence space
Tóm tắt
In this paper, we introduce Cesàro–Gamma matrix that exhibits the structure of both the Cesàro and Gamma matrices. We study the domain of this new matrix in the space
$$\ell _p$$
(
$$1\le p\le \infty$$
). By this new matrix, we obtain a factorization for the infinite Hilbert matrix, based on the Cesàro matrix of order
$$\lambda$$
, of the form
$$H=B^\lambda C^\lambda$$
. As a second application of this operator, we obtain a factorization for the Cesàro matrix of order
$$\lambda$$
of the form
$$C^{\lambda +\tilde{\lambda }}=R^{\lambda , \tilde{\lambda }+1}C^{\tilde{\lambda }}$$
, which results in a factorization for the Cesàro matrices of the form
$$C^\lambda =S^{\lambda ,\tilde{\lambda }} C^{\tilde{\lambda }}.$$
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