​​July 2021, Vol. 6, No. 7, pp. 101-104. 

​​​On Orthogonality Conditions for the Range and Kernel of Generalized Derivations

W. L. Otae¹, N. B. Okelo¹,*, M. B. Nzimbi², O. Ongati¹
¹Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya
²Department of Mathematics, University of Nairobi-Kenya.

​​​*Corresponding author’s e-mail:bnyaare@yahoo.com

​Abstract

​In the present work, authors reported characterization of orthogonality conditions of the range and the kernel of generalized derivations whose implementing operators are hyponormal in normed spaces. We have shown that if A is a subnormal operator on H with a cyclic vector and if T is abounded linear operator on H which commutes with A and A* then T is hyponormal. Moreover, the range and the kernel of generalized derivations are orthogonal when the inducing operators are from the norm ideal.

Keywords: Orthogonality; Derivations; Range; Kernel.

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International Journal of Modern Science and Technology

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ISSN 2456-0235