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Products of operator ideals and extensions of Schatten classes

✍ Scribed by Thomas Kühn; Mieczysław Mastyło

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
165 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 2 → E. We show that for a large class of 2-convex symmetric Banach sequence spaces the product ideal ΠE,2 • S a q,s is an extension of the Schatten class SF 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) n 1/p , then ΠE,2 • Πq is an extension of the Schatten class Sr,q.

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