BOHR OPERATOR ON OPERATOR VALUED POLYANALYTIC FUNCTIONS ON SIMPLY CONNECTED DOMAINS

Abstract In this article, we study the Bohr operator for operator-valued subordination class $S(f)$ consisting of holomorphic functions subordinate to f in unit disk $\mathbb {D}:=\{z \in \mathbb {C}: |z|<1\}$ , where $f:\mathbb {D} \rightarrow \mathcal {B}(\mathcal {H})$ is and $\mathcal algebra bounded linear operators on a complex Hilbert space {H}$ . We establish several results, which can be viewed as analogs couple interesting results from scalar-valued settings. also obtain von Neumann-type inequality analytic self-mappings {D}$ fix origin. Furthermore, extensively inequalities polyanalytic certain proper simply connected domains {C}$ radius form $F(z)= \sum _{l=0}^{p-1} \overline {z}^l \, f_{l}(z) $ $f_{0}$ an convex biholomorphic function, starlike function