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

Research Article · Biotechnology & Bioeng. · Volume 4, Issue 9 · Sep 2019 · Pages 238–245

Orthogonality of Finite Rank Generalized Derivations

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

  • M. F. C. Kaunda: 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.
  • Omolo Ongati: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.

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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