Abstract
Absolutely varphi -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 -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 . 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 -summing operators on the Hilbert space ell _2 are characterized in terms of its approximation numbers.
Highlights
The motivation for this paper comes from the theory of operator ideals
In this article we study a class of absolutely φ-summing operators between
We investigate the relationship between vector-valued inequalities associated to absolutely φ-summing operators
Summary
The motivation for this paper comes from the theory of operator ideals. The notion of absolutely p-summing operator has a long history and concerns an important ideal of operators between Banach spaces. In what follows we will prove vector-valued inequalities for φ semi-integral operators generated by Orlicz functions satisfying some minor conditions.
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