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

Research Article · Biotechnology & Bioeng. · Volume 6, Issue 7 · Jul 2021 · Pages 101–104

On Orthogonality Conditions for the Range and Kernel of Generalized Derivations

W. L. Otae, N. B. Okelo, M. B. Nzimbi, O. Ongati

  • W. L. Otae: Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya
  • N. B. Okelo: Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya
  • M. B. Nzimbi: Department of Mathematics, University of Nairobi-Kenya.
  • O. Ongati: Department of Pure and Applied Mathematics, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya

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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