The Conditions under Which the Norm of Elementary Operator of Length Two Is Expressible In Terms Of Its Co-Efficient Operators in Tensor Product of -Algebra: An Application of Stampflis Maximal Numerical Range

Abstract

Many researchers have studied the properties of elementary operators, including numerical ranges, spectrum, compactness and rank, in great depth, and numerous results have been obtained using different approaches such as spectral resolution theorem, tracial geometric mean, finite rank operator and Stampfli's maximal numerical range. The conditions under which the norm property can be expressed in terms of its coefficient operators, has also been considered in many studies but remains unresolved. This study sought to determine the application of Stampfli's maximal numerical range by determining the conditions under which the norm of the elementary operator of length two can be expressed in terms of its coefficient operators. The study used Stampfli's maximal numerical range and techniques of tensor products of -Algebras to express the norm of an elementary operator of length two in terms of its coefficient operators. Finally, the study used Cauchy Schwartz's inequality to determine the upper bound. In this study, the norm of the elementary operator is expressed in terms of coefficient operators and shown to be, . where are fixed elements in the set of bounded linear operator of tensor product of Hilbert space and . Theme: Integration of innovation and technology for sustainable interdisciplinary collaboration