Linear isometries between real Banach algebras of continuous complex-valued functions
Summary: Let \(X\) and \(Y\) be compact Hausdorff spaces, and let \(\tau\) and \(\eta\) be topological involutions on \(X\) and \(Y\), respectively. In [Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 30, No. 2, 343--356 (1991; Zbl 0764.46051)], \textit{S. H. Kulkarni} and \textit{S. Arundhathi} characterized linear isometries from a real uniform function algebra \(A\) on \((X,\tau)\) onto a real uniform function algebra \(B\) on \((Y,\eta)\) applying their Choquet boundaries and showed that these mappings are weighted composition operators. In this paper, we characterize all onto linear isometries and certain into linear isometries between \(C(X,\tau)\) and \(C(Y,\eta)\) applying the extreme points in the unit balls of \(C(X,\tau)^*\) and \(C(Y,\eta)^*\).
scientific article; zbMATH DE number 6371130