Abstract Let $\mathcal {B}(\mathcal {H})$ be the algebra of all bounded linear operators on a complex Hilbert space {H}$ . In this paper, we first establish several sharp improved and refined versions Bohr’s inequality for functions in class $H^{\infty }(\mathbb {D},\mathcal {H}))$ analytic from unit disk $\mathbb {D}:=\{z \in \mathbb {C}:|z|<1\}$ into For complete circular domain $Q \subset...
