SOME STABLE OPERATOR IDEALS

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.