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

Research Article · Mathematical Sciences · Volume 2, Issue 3 · Mar 2017 · Pages 81–84

Characterization of Norm Inequalities for Elementary Operators

B. O. Okello, N. B. Okelo, O. Ongati

  • B. O. Okello: 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

Studies on the norms of the elementary operators on JB*-algebras Prime C*-algebras, Calkin algebras and standard operator algebras has been considered. In this paper, we characterize norm inequalities for Jordan elementary operators on C*-algebras. The results show that if H is an infinite dimensional complex Hilbert space and B(H) the C*-algebra of all bounded linear operators on H, then for a Jordan elementary operator U : B(H) → B(H) defined by: U(T) = PTQ + QTP for all T ϵ B(H) and Pi;Qi fixed in B(H), ║U(T)║ ≤ 2║P║║Q║. Moreover, if Pi and Qi are diagonal operators induced by {  ni} and {βni}respectively and H an infinite dimensional complex Hilbert space then U is bounded and║U║ = (Σn{Σli=1|  ni |2| βni |2})1/2.

Keywords

Norm; C*-algebra; Elementary operator; Hilbert space

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