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Reflexivity of isometries of order $n$

Volume 159 / 2020

Abdullah Bin Abu Baker Colloquium Mathematicum 159 (2020), 223-230 MSC: Primary 47L05; Secondary 46B20. DOI: 10.4064/cm7432-12-2018 Published online: 14 November 2019


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 $C_0(\Omega ,X)$.


  • Abdullah Bin Abu BakerDepartment of Applied Sciences
    Indian Institute of Information Technology Allahabad
    Jhalwa, Allahabad 211015, U.P., India

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