Operator revision of a Ky Fan type inequality

Jamal Rooin, Akram Alikhani

Let $\mathcal{H}$ be a complex Hilbert space and $A,B\in \mathbb{B}(\mathcal{H})$ such that $0<A,B\le \frac{1}{2}I$. Setting $A^{\prime }:=I-A$ and $B^{\prime }:=I-B$, we prove $$ A'\nabla_λB'-A'!_λ…