Boundary curvature of the numerical range of self-inverse operators

In this article, firstly we investigate some properties of the boundary curvature of the numerical range. In the next, we define M(T) as the smallest constant such that dist(\lambda,\sigma(T))\leq M(T) R_\lambda (T), for all \lambda \in \partial W(T), where R_\lambda (T), the radius curvature at the point \lambda, is defined. Also, we investigate for non-convexoid T, M(T)=\sup\frac{dist(\lambda,\sigma(T))}{R_{\lambda}(T)}, where the supremum on the right-hand side is taken along all points \lambda\in \partial W(T) with finite non-zero curvature. Finally, the value of M(T) will be calculated for the self-inverse operators.

کلیدواژه ها:

Boundary Curvature ، Numerical range ، Self-Inverse Operators