K-Convexity and Duality for Almost Summing Operators

For a fixed sequence f. = (fn ) of independent identically distributed symmetric random variables with , we introduce the notion of Kf. -convex Banach space and the notions of (fn )-bounding and (fn )-converging operators acting between Banach spaces. It is shown that the dual of the space of (fn )-converging operators between a Hilbert space and a Kf. -convex Banach space admits a precise description in terms of trace duality. The obtained results recover similar formulations for almost summing and γ-Radonifying operators.