Mohamed Chraibi kaadoud

Closed numerical ranges

Let $ x=(x_{n})_{n} $ be a bounded complex sequence and let $M_{x} = \sup_n |x_n|$. By using a normaloid operator related to the sequence $ x=(x_{n})_{n} $, we prove that $$ \sup_{λ\in \mathbb{C}, |λ| \leq M_x} \sup_n |x_n+λ| = 2M_x.$$