On Properties of Derivations in Normed Spaces

Benard Okelo
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Benard Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya

Academic Journal of Applied Mathematical Sciences, 2020, vol. 6, issue 6, 77-79

Abstract: Let δ: Cp→Cp be normal, then the linear map ( ) attains a local minimum at Cp if and only if z Cp such that ( ) ( ( )≥0. Also let Cp, and let ( ) have the polar decomposition ( ) ( ) then the map attains local minimum on Cp at T if and only if ( ). Regarding orthogonality, let S Cp and let N(S) have the polar decomposition N(S) =U|N(S)|, then ( ) ( ) for X Cp if ( ) . Moreover, the map has a local minimum at if and only if ( )( ( )) for y . In this paper, we give some results on local minimum and orthogonality of normal derivations in Cp-Classes. We employ some techniques for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson.

Keywords: Hilbert space; Local minimum; Orthogonality and Schatten-p class. (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:arp:ajoams:2020:p:77-79

DOI: 10.32861/ajams.66.77.79

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