English

Closed numerical ranges

Functional Analysis 2019-01-29 v3

Abstract

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

Cite

@article{arxiv.1805.09939,
  title  = {Closed numerical ranges},
  author = {Abderrahim Baghdad and Mohamed Chraibi kaadoud},
  journal= {arXiv preprint arXiv:1805.09939},
  year   = {2019}
}
R2 v1 2026-06-23T02:07:52.350Z