We will discuss properties of ideal φ-summing operators generated by Orlicz spaces. We will show asymptotic estimates of φ-summating norms of finite-dimensional operators as well as diagonal operators between certain Banach sequence spaces. The proof is based on the description of the Rademacher spaces in this class of Orlicz spaces, which is proved by interpolation methods. As an application, we obtain the characterisation of φ-summing operators on the Hilbert spacein terms of approximation numbers.
Mieczyslaw Mastyło
Adam Mickiewicz University, Poznań