Closed numerical ranges

Abderrahim Baghdad; Mohamed Chraibi kaadoud

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arXiv · 1805.09939

Closed numerical ranges

Abderrahim Baghdad·Mohamed Chraibi kaadoud

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Abstract

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 $$ \sup_{\lambda \in \mathbb{C}, |\lambda| \leq M_x} \sup_n |x_n+\lambda| = 2M_x.$$

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Abderrahim Baghdad, Mohamed Chraibi kaadoud. 2018-05-25. Closed numerical ranges. https://arxiv.org/abs/1805.09939

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