Inequalities for the spectral radius and essential spectral radius of positive operators on Banach sequence spaces

We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric mean of (infinite or finite) nonnegative matrices that define positive operators on Banach sequence spaces. Some of these inequalities complement the known inequalities and some of them refine known inequalities. Several inequalities appear to be new even in the finite dimensional case.