ON The SM -Operators

Abstract

This is a partial part of our results in studying generalization of Hilbert-Schmidt and Carleman operators in Banach spaces. This problem can be done if we preserve some intrinsic properties of Hilbert spaces involved; for examples, reflexivity and separability. The result of the generalization of Hilbert-Schmidt operator will be called SM-operator. Infact, almost all of properties of the SM-operator preserve almost all of properties of the Hilbert-Schmidt operators. The application on some classical Banach spaces will appear in the next publications.

Keywords: Orthonormal Schauder bases,separable and reflexive Banach spaces, Hilbert- Schmidt operator