Summing norms of identities between unitary ideals |
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Authors: | Andreas Defant Mieczysław Mastyło Carsten Michels |
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Institution: | 1. Fk. 5, Inst. f. Mathematik, Carl von Ossietzky Universit?t Oldenburg, Postfach 2503, D-26111, Oldenburg, Germany 2. Faculty of Mathematics and Computer Science, A. Mickiewicz University and Institute of Mathematics, Polish Academy of Sciences (Poznań branch), Umultowska 87, 61-614, Poznań, Poland
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Abstract: | Based on abstract interpolation, we prove asymptotic formulae for the (F,2)-summing norm of inclusions id: , where E and F are two Banach sequence spaces. Here, stands for the unitary ideal of operators on the n-dimensional Hilbert space whose singular values belong to E, and for the Hilbert-Schmidt operators. Our results are noncommutative analogues of results due to Bennett and Carl, as well as
their recent generalizations to Banach sequence spaces. As an application, we give lower and upper estimates for certain s-numbers of the embeddings id: and id: . In the concluding section, we finally consider mixing norms.
The second named author was supported by KBN Grant 2 P03A 042 18. |
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Keywords: | Absolutely summing operators Unitary ideals Approximation numbers Mixing operators |
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