Unitary solutions of the equation cu+u*c=2d Original Research Article

Given self-adjoint c and d the existence of unitary solutions of the equation cu+u*c=2d is studied in a unital C*-algebra image . Assuming that c is invertible necessary and sufficient conditions in algebra B(H) are proved. If image , c=c*, d=d* it is proved that K(λ)=λ2e+2λd+c2greater-or-equal, slantedδe>0 guaranties the existence of the solutions in image as well as the factorizations of K(λ) of the form K(λ)=(λe−z)(λe−z*), image . Also the classification of all unitary solutions is given.