E-mail: roshdi@ju.edu.jo
Abstract. Let $\Pi$ be an operator ideal in the sense of Pietsch. Then $\Pi$ is called stable if whenever $T_1$ and $T_2\in \Pi$ then $T_1 \overset{\vee }\to\otimes T_2 \in \Pi$. 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.
AMSclassification. Primary 47B10, Secondary 47D50
Keywords. Operator ideal, stable.