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

Research Article · Mathematical Sciences · Volume 2, Issue 10 · Oct 2017 · Pages 337–340

On Characterization of Normal Derivations

B. O. Owino, N. B. Okelo, O. Ongati

  • B. O. Owino: 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.
  • O. Ongati: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P.O. Box 210-40601, Bondo-Kenya.

Abstract

In the present paper we established orthogonality of normal derivations in Cp-Classes. We employ some results for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson. Let T be a compact operator and φ be the subspace where T attains its norm, let φϵ be the set of vectors from Cp-class which forms an angle less or equal to ϵ with φ. We show that two operators are orthogonal if their inner product is zero.

Keywords

Banach space; Hilbert space; Gateaux derivative; Orthogonality; Schatten-p Class

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