Muiruri, Peter GKingangi, DenisMusundi, Sammy Wabomba2020-10-012020-10-012018-01International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 6, Issue 6, 2018, PP 15-222347-3142https://www.arcjournals.org/pdfs/ijsimr/v6-i6/2.pdfhttp://repository.chuka.ac.ke/handle/chuka/892In this paper, we determine the norm of an elementary operator in a tensor product. More precisely, we investigate the bounds of the norm of a basic elementary operator in a tensor product. We employ the techniques of tensor products and finite rank operators to express the norm of an elementary operator in terms of its coefficient operators. We also show that the norm of a basic elementary operator on is expressible in terms of the norms of basic elementary operators on and B(HOK) is expressible in terms of the norms of basic elementary operators on B(H) and B(K) .enBasic Elementary OperatorFinite rank Operator and Tensor productArticle