On The Norm of Finite Length Elementary Operator in Tensor Product of C*-Algebras

Abstract

Many properties of Elementary operators, including spectrum, numerical ranges, compactness, rank, and norm have been studied in depth and some results have been obtained. However, little has been done in determining the norm of finite length elementary operator in tensor product of C*-algebras. The norm of basic elementary operator in tensor product of C*-algebras have been determined and results obtained. This paper determines the norm of finite length elementary operator in a tensor product of C*-algebras. More precisely, the bounds of the norm of finite length elementary operator in a tensor product of C*-algebras are investigated. The paper employs the techniques of tensor products and finite rank operators to express the norm of an elementary operator in terms of its coefficient operators.