An operator ideal generated by Orlicz spaces

Abstract

Abstract Absolutely $$\varphi $$φ-summing operators between Banach spaces generated by Orlicz spaces are investigated. A variant of Pietsch’s domination theorem is proved for these operators and applied to prove vector-valued inequalities. These results are used to prove asymptotic estimates of $$\pi _\varphi $$πφ-summing norms of finite-dimensional operators and also diagonal operators between Banach sequence lattices for a wide class of Orlicz spaces based on exponential convex functions $$\varphi $$φ. The key here is the description of a space of coefficients of the Rademacher series in this class of Orlicz spaces, proved via interpolation methods. As by-product, some absolutely $$\varphi $$φ-summing operators on the Hilbert space $$\ell _2$$ℓ2 are characterized in terms of its approximation numbers.