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SOME STABLE OPERATOR IDEALS

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*Roshdi Khalil and Majeda Aziz*

**Address.** University of Jordan, Faculty of Science, Department of
Mathematics, Amman, JORDAN
**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.