INDEXED IN 

ISSN 2456-0235

ISSN 2456-0235

International Journal of Modern Science and Technology

​​​​​International Journal of Modern Science and Technology, Vol. 2, No. 3, 2017, Pages 81-84. 

​

​Characterization of Norm Inequalities for Elementary Operators

B. O. Okello, 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
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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