grandes-ecoles 2022 Q22

grandes-ecoles · France · x-ens-maths-c__mp Sequences and Series Proof of Inequalities Involving Series or Sequence Terms
We assume that $|\lambda| \notin \{0,1\}$ and that $\rho(f) > 0$. We consider the series $H \in O_2$ from part E. Show that the series $H$ satisfies $\hat{H} \prec \frac{1}{\omega} \hat{F} \circ (I + \hat{H})$.
We assume that $|\lambda| \notin \{0,1\}$ and that $\rho(f) > 0$. We consider the series $H \in O_2$ from part E. Show that the series $H$ satisfies $\hat{H} \prec \frac{1}{\omega} \hat{F} \circ (I + \hat{H})$.