ISSN 2456-0235

International Journal of Modern Science and Technology

INDEXED IN 

​​​​​​​September 2019, Vol. 4, No. 9, pp 238-245. 

​​​Orthogonality of Finite Rank Generalized Derivations

M. F. C. Kaunda, N. B. Okelo*, Omolo 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

​Let H be an infinite dimensional Hilbert space. In this paper, we employ operator techniques, polar decomposition, Halmos generalization formula and derivation inequalities to establish orthogonality in normed spaces. An operator A is hyponormal and B* is m-hyponormal if T is a generalized nilpotent hyponormal operator. Properties of operators in the closure of the range of the inner derivation have been used to establish orthogonality of finite rank derivations.

Keywords: Hyponormal operators; Generalized derivations; Commutator; Orthogonality; Finite rank.

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