Numerical Ranges and Spectral Sets: the unbounded case

Abstract

It is known that, if $\hat{I}\text{c◯}$ $\subset$ C is a convex set containing the numerical range of an operator A, then $\hat{I}\text{c◯}$ is a C $\hat{I}\text{c◯}$ -spectral set for A with C $\hat{I}\text{c◯}$ $\le$ 1+ $\sqrt$ 2. We improve this estimate in unbounded cases.