International Journal of Nonlinear Analysis and Applications

Boundary curvature of the numerical range of self-inverse operators

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75918 Iran

2 Department of Mathematics, College of Sciences, Yasouj Univer- sity, Yasouj, 75918, Iran

Abstract

In this article, firstly we investigate some properties of the boundary curvature of the numerical range. In the next, we define $M(T)$ as the smallest constant such that $dist(\lambda,\sigma(T))\leq M(T) R_\lambda (T),$ for all $\lambda \in \partial W(T)$, where $R_\lambda (T)$, the radius curvature at the point $\lambda$, is defined. Also, we investigate for non-convexoid $T$, $M(T)=\sup\frac{dist(\lambda,\sigma(T))}{R_{\lambda}(T)}$, where the supremum on the right-hand side is taken along all points $\lambda\in \partial W(T)$ with finite non-zero curvature. Finally, the value of $M(T)$ will be calculated for the self-inverse operators.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 5
May 2025
Pages 35-42
  • Receive Date: 31 January 2024
  • Revise Date: 09 April 2024
  • Accept Date: 29 April 2024