International Journal of Modern Science and Technology · ISSN 2456-0235

Research Article · Biotechnology & Bioeng. · Volume 3, Issue 1 · Jan 2018 · Pages 10–16

Norms of Normally Represented Elementary Operators

A. M. Wafula, N. B. Okelo, O. Ongati

  • A. M. Wafula: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.
  • N. B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.
  • O. Ongati: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.

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

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