Products of operator ideals and extensions of Schatten classes | Zendy

Kühn Thomas | Zendy; Mastyło Mieczysław | Zendy

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Products of operator ideals and extensions of Schatten classes

Author(s) -

Kühn Thomas,

Mastyło Mieczysław

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200713700

Subject(s) - mathematics , banach space , ideal (ethics) , lorentz space , class (philosophy) , product (mathematics) , sequence (biology) , extension (predicate logic) , operator (biology) , regular polygon , space (punctuation) , combinatorics , pure mathematics , function (biology) , strictly singular operator , discrete mathematics , lorentz transformation , finite rank operator , operator space , geometry , epistemology , classical mechanics , transcription factor , programming language , physics , gene , philosophy , repressor , artificial intelligence , chemistry , computer science , biology , genetics , biochemistry , evolutionary biology , linguistics

We study relations between Schatten classes and product operator ideals, where one of the factors is the Banach ideal Π E ,2 of ( E , 2)‐summing operators, and where E is a Banach sequence space with ℓ 2 ↪ E . We show that for a large class of 2‐convex symmetric Banach sequence spaces the product ideal Π E ,2 ○ a q , 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 λ E ( n ) ≈ n 1/ p , then Π E ,2 ○ Π q is an extension of the Schatten class r , q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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