ON THE NORM OF JORDAN ELEMENTARY OPERATOR IN TENSOR PRODUCT OF C*-ALGEBRAS

Abstract

The norm property of different types of Elementary operators has attracted a lot of researchers due to its wide range applications in functional analysis. From available literature the norm of Jordan elementary operator has been determined in C*-algebras, JB*-algebras, standard operator algebra and prime JB*-triple but not much has been done in tensor product of C*- algebras. This paper, dealt with the norm of Jordan elementary operator in a tensor product of C*-algebras. More precisely, the paper investigated the bounds of the norm of Jordan elementary operator in a tensor product of C*-algebras and obtained that ∥ 𝑼𝑨⨂𝑩,𝑪⨂𝑫 ∥= 𝟐 ∥ 𝑨 ∥∥ 𝑩 ∥∥ 𝑪 ∥∥ 𝑫 ∥. The concept of finite rank operator and properties of tensor product of Hilbert spaces and operators and vectors in Hilbert spaces were used to achieve the paper’s objective