Abstract
We study relations between Schatten classes and product operator ideals, where one of the factors is the Banach ideal ΠE,2 of (E, 2)-summing operators, and where E is a Banach sequence space with l2 ↪ E. We show that for a large class of 2-convex symmetric Banach sequence spaces the product ideal ΠE,2 ○ aq,s is an extension of the Schatten class F with a suitable Lorentz space F. As an application, we obtain that if 2 ≤ p, q < ∞, 1/r = 1/p + 1/q and E is a 2-convex symmetric space with fundamental function λE(n) ≈ n1/p, then ΠE,2 ○ Πq is an extension of the Schatten class r,q (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have