SOME PROPERTIES OF THE NON LINEAR OPERATOR MAPPINGS

Khaleel, Ahlam Jameel
Mohisn, Salim Dawood

MAGISTRA
Vol 26, No 88 (2014): Magistra Edisi Juni

In this paper, we discuss and study some properties of the mapping
,)( **
AXXAXA  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  where B is bounded
linear operator, as well as study the mapping *****
)()()( AXXAAXXAX nn
A   , with given necessary
and sufficient condition to solvability of the operator equation .)( BXA 