SOME PROPERTIES OF THE NON LINEAR OPERATOR MAPPINGS - Khaleel, Ahlam Jameel; Mohisn, Salim Dawood (MAGISTRA, 2014)
In this paper, we discuss and study some properties of the mapping ,)( ** AXXAXA ï«ï½ï defined for bounded nonlinear operators X on a complex Hilbert space. Also, we study the range of this mapping and solvability of the operator equation ,)( BXA ï½ï where B is bounded linear operator, as well as study the mapping ***** )()()( AXXAAXXAX nn A ï¡ï´ ï«ï«ï½ , with given necessary and sufficient condition to solvability of the operator equation .)( BXA ï½