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In this article, we study the Bohr operator for the operator valuedsubordination class $S(f)$ consisting of holomorphic functions subordinate to$f$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$, where$f:\mathbb{D} \rightarrow \mathcal{B}(\mathcal{H})$ is holomorphic and$\mathcal{B}(\mathcal{H})$ is the algebra of bounded linear operators on acomplex Hilbert space $\mathcal{H}$. We establish several subordinationresults, which can be viewed as the analogues of a couple of interestingsubordination results from scalar valued settings. We also obtain a vonNeumann-type inequality for the class of self-analytic mappings of the unitdisk $\mathbb{D}$ which fix the origin. Furthermore, we extensively study Bohrinequalities for operator valued polyanalytic functions in certain propersimply connected domains in $\mathbb{C}$. We obtain Bohr radius for theoperator valued polyanalytic functions of the form $F(z)= \sum_{l=0}^{p-1}\overline{z}^l \, f_{l}(z) $, where $f_{0}$ is subordinate to an operatorvalued convex biholomorphic function, and operator valued starlikebiholomorphic function in the unit disk $\mathbb{D}$.

Bohr operator on opertor valued polyanalytic functions on simply connected domains