## 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.)

### Keywords:

operator ideal; stability
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