On the Norm of Jordan Elementary Operators in Tensor Product of C ∗ -Algebras

Abstract

Elementary operators have been studied over years, with their norms being of significant interest in operator theory. The study includes the derivation of formulas that describe norms in terms of their coefficient operators, which is traced back to Stampfli`s Theorem that used the property of Numerical range as a foundation for the study of norms. Other properties of Elementary operators have been studied ever since, but little is known on Jordan Elementary operators in tensor products of C ∗ - algebras. This paper aims to extend the determination of norms of Jordan Elementary operators in the tensor product of C ∗ - algebra by determining the lower bound of the norm using the maximal numerical range by employing the technique of tensor product, finite rank operator and inner product. A lower bound of Jordan elementary operator in tensor product of C ∗algebras

is obtained.