Algebraic Reflexivity of the set of n-Isometries on C(X,E)

TL;DR

This paper investigates the algebraic reflexivity of n-isometries on spaces of continuous functions, establishing that reflexivity properties extend from isometries to n-isometries and generalized bi-circular projections.

Contribution

It proves that algebraic reflexivity of isometry groups implies reflexivity of n-isometries and generalized bi-circular projections on C(X,E).

Findings

Reflexivity of isometry groups implies reflexivity of n-isometries.

Established algebraic reflexivity of generalized bi-circular projections.

Extended reflexivity results to spaces of continuous functions with Banach space codomain.

Abstract

We prove that if the group of isometries of C(X,E) is algebraically reflexive, then the group of n-isometries is also algebraically reflexive. Here, X is a compact Hausdorff space and E is a Banach space. As a corollary to this, we establish the algebraic reflexivity of the set of generalized bi-circular projections on C(X,E).