Composition of the Cesàro Operator and Its Transpose.

In this study, by the composition of Cesàro operator with its transpose, we obtain two interesting operators which are Hilbert’s commutants. Moreover, the ℓ p norm of those operators has been computed in this study which results in obtaining some new inequalities, one of them is the generalization of Hardy’s inequality. As an application, we have also computed the norm of well-known operators on the matrix domains associated with those matrices. [ABSTRACT FROM AUTHOR]