Generalized approximation and estimation of entropy numbers

In this article, we generalize an approximation result known for entropy numbers of operators. We show that the entropy numbers of a bounded linear operator can be approximated by those of certain truncations of the operator under very general assumptions. Using the relation between the entropy numbers and the inner entropy numbers of bounded sets, we derive estimates for entropy numbers of bounded linear operators. We also obtain new estimates for specific types of operators, including the diagonal operators between sequence spaces, and use these estimates to illustrate the convergence result proved.