Norm estimates for matrix operators between Banach spaces

We study norm estimates of matrix operators between Banach spaces. In particular, we prove a general variant of the Hardy–Littlewood result on lower estimate for norms of operators between ℓp-spaces and show applications to Calderón–Lozanovskii sequence lattices. We also provide estimates for norms of radially generated operators from abstract Hardy spaces to Banach sequence lattices. Likewise we prove the mean convergence theorem in abstract Hardy spaces and show general examples of radially generated operators.