A functional calculus for numerical ranges
Guoxing Ji · Journal of Baoji University of Arts and Sciences · 2011
Aim It is described that two bounded linear operators A,B on a complex Hilbert space H are multiples of identity.Methods The properties of analytic function and block of operators.Results and Conclusion It is proved that for any bounded linear operators A and B on a complex Hilbert space H and a non-linear analytic function g on the numerical range W(B) of B,if(Ax,x)=g((Bx,x)) for all unit vectors x∈H,then both A and B are multiples of identity.