Approximately angle preserving mappings

Abstract

In this paper, we present some characterizations of linear mappings, which preserve vectors at a specific angle. We introduce the concept of $(\epsilon ,c)$-angle preserving mappings for $|c|<1$ and $0\le \epsilon <1+|c|$. In addition, we define $\hat{\epsilon }(T,c)$ as the ``smallest'' number $\epsilon$ for which $T$ is $(\epsilon ,c)$-angle preserving mapping. We state some properties of the function $\hat{\epsilon }(.,c)$, and then propose an exact formula for $\hat{\epsilon }(T,c)$ in terms of the norm $\Vert T\Vert$ and the minimum modulus $[T]$ of $T$. Finally, we characterize the approximately angle preserving mappings.

12 pages, to appear in Bull. Austral. Math. Soc

References in corpus (1)

• Angle Preserving Mappings