On Properties of Derivations in Normed Spaces

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.