Resolvents

R_T\colon\mathcal{C}_1 \to H_0(\boldsymbol{C}\setminus\sigma(T)), L\mapsto\operatorname{tr}L(z - T)^{-1}.

R_T^*\colon H(\sigma(T))\to\mathcal{B}(\mathcal{H}) is the Riesz functional calculus.