Homological dimensions of analytic Ore extensions

If $A$ is an algebra with finite right global dimension, then for any automorphism $\alpha$ and $\alpha$-derivation $\delta$ the right global dimension of $A[t;\alpha ,\delta ]$ satisfies [ $\text{rgld}$ , A \le $\text{rgld}$ , A[t; \alpha, \delta] \le $\text{rgld}$ , A

• 1. ] We extend this result to the case of holomorphic Ore extensions and smooth crossed products by $\mathbb{Z}$ of $\widehat{\otimes }$-algebras.