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International Journal of Modern Science and Technology

​​​​​​January 2018, Vol. 3, No 1, pp 10-16. 

​​​Norms of Normally Represented Elementary Operator

A. M. Wafula, N. B. Okelo, O. Ongati
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology,
P.O. Box 210-40601, Bondo-Kenya.
​​​*Corresponding author’s e-mail: bnyaare@yahoo.com

​Abstract

​The norm problem involves finding the formula describing the norm from the coefficients of the elementary operators. Upper estimate of the norm has been easy to find but estimating the norm from below has been proven difficult in general. In this study, we considered a special type of elementary operators called normally represented elementary operators. Some of our results show that the norm of an elementary operator is equal to the largest singular value of the operator itself i.e. Si(M) = ∥M∥ and also if UA,B = A ⊗h B + B ⊗h A is normally represented, then ∥UA,B∥Inj  ≥ 2(√(2 – 1))∥A∥∥B∥.

Keywords: Norms; Elementary operator; Normally represented elementary operator; Norm-attainable operators.

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ISSN 2456-0235