The Distance From a Point to a Compact Convex Set

Authors

  • Mohammad Taghi Heydari

Keywords:

compact convex set . distance . Numerical range.

Abstract

Let $K$ be a compact convex subset of the plane and $\lambda \in \mathbb{C}\backslash K$, then $$ dist(\lambda ,K)=\|(\lambda -N_{\mu})^{-1}\|^{-1},$$ where $\mu$ is the Lebesgue measure concentrated on $K$ and $N_{\mu}$ be the multiplication operator on $L^{2}(\mu)$.

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How to Cite

Heydari, M. T. (2014). The Distance From a Point to a Compact Convex Set. European Journal of Pure and Applied Mathematics, 7(2), 129–130. Retrieved from https://ejpam.com/index.php/ejpam/article/view/1882