On Eigenvalues and Boundary Curvature of the Numerical Rang of Composition Operators on Hardy Space

摘要

For a bounded linear operator A on a Hilbert space H, let M(A) be the smallest possible constant in the inequality . Here, p is a point on the smooth portion of the boundary of the numerical range of A. is the radius of curvature of at this point and ?is the distance from p to the spectrum of A. In this paper, we compute the M(A) for composition operators on Hardy space H2.