Reflexivity of isometries of order $n$
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 223-230
MSC: Primary 47L05; Secondary 46B20.
DOI: 10.4064/cm7432-12-2018
Published online: 14 November 2019
Abstract
We prove that if the group of isometries on $C_0(\Omega ,X)$ is algebraically reflexive, then the set of isometries of order $n$ on $C_0(\Omega ,X)$ is also algebraically reflexive. Here, $\Omega $ is a first countable locally compact Hausdorff space, and $X$ is a Banach space having the strong Banach–Stone property. As a corollary, we establish the algebraic reflexivity of the set of generalized bi-circular projections on $C_0(\Omega ,X)$.
