Operator ideals generated by strongly Lorentz sequence spaces

摘要

We introduce and study the new ideal of strongly Lorentz summing operators between Banach spaces generated by strongly Lorentz sequence spaces to study the adjoints of the Lorentz summing operators. We also prove the related dual result: an operator is Lorentz summing if and only if its adjoint is strongly Lorentz summing. Some examples, counterexamples and connections with the theory of absolutely summing operators are given.