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Some stable operator ideals. (English) Zbl 1068.47086

Summary: Let \(\Pi \) be an operator ideal in the sense of A. Pietsch. Then \(\Pi \) is called stable if whenever \(T_1\) and \(T_2 \in \Pi \) then \(T_1 \overset \vee \otimes T_2\in \Pi \). In this paper, we study the stability of some operator ideals. In particular, we prove that the ideals of \(r\)-nuclear and \(r\)-integral operators are stable. Further, we study the stability of some hulls of some operator ideals. Using these results, we give a new proof for the stability of \(p\)-summing operators.

MSC:

47L20 Operator ideals
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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