Functional calculus for a bounded $C_0$-semigroup on Hilbert space

Loris Arnold, Christian Le Merdy

We introduce a new Banach algebra $\mathcal{A}({\mathbb{C}}_{+})$ of bounded analytic functions on ${\mathbb{C}}_{+}=\{z\in \mathbb{C}:\mathrm{Re}(z)>0\}$ which is an analytic versio…