Products of operator ideals and extensions of Schatten classes |
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| Authors: | Thomas Kühn Mieczysław Mastyło |
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| Affiliation: | 1. Fakult?t für Mathematik und Informatik, Mathematisches Institut, Universit?t Leipzig, Johannisgasse 26, 04103 Leipzig, Germany;2. Phone: +49 341 97 32 148, Fax: +49 341 97 32 199;3. Faculty of Mathematics and Computer Science, Adam Mickiewicz University;4. and Institute of Mathematics, Polish Academy of Sciences Poznań branch, Umultowska 87, 61‐614 Poznań, Poland |
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| 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 ?2 ? 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) |
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| Keywords: | Symmetric Banach sequence spaces Banach operator ideals approximation numbers Schatten classes |
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