Composition of (E,2)-summing operators

Abstract

Abstract. The Banach operator ideal of (q, 2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E, 2)-summing operators, E a symmetric Banach sequence space.

Absolutely summing multilinear operators: a panorama

“…In the 80's the part of the focus of the investigation related to absolutely summing operators was naturally moved to the nonlinear setting, which will be treated in the next sections. However the linear theory is still alive and there are still interesting problems being investigated (see, for example, [32,50]). For recent results we mention [21,25,51,52]:…”

Products of operator ideals and extensions of Schatten classes

“…For the sake of completeness we include a proof (cf. [4] P r o o f. Note that if G is a symmetric quasi-normed sequence space, then for any x = (x n ) ∈ G, we have x * = y + z with y = n x * 2n−1 e 2n−1 and z = n x * 2n e 2n in ω. Since y * = (x * 2n−1 ) ∈ G and z * ≤ y * , we get z * ∈ G and also z ∈ G with z G ≤ y G .…”