Factorization of the infinite Hilbert and Cesàro operators

Abstract

In this research we introduce several factorization for the infinite Hilbert and Ces`aro operators based on Ces`aro and Gamma operators. As a result we obtain several interesting inequalities; some of those are the generalized version of two well-known Hilbert and Hardy's inequalities. Furthermore, we obtain some inclusion relations and compute the norm of these operators on several matrix domains.