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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Published

2014-05-08

Issue

Vol. 7 No. 2: (April 2014)

Section

Topology

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How to Cite

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