Biseparating maps on Fréchet function algebras (Q1936458)

Summary: Let \(A\) and \(B\) be strongly regular normal Fréchet function algebras on compact Hausdorff spaces \(X\) and \(Y\), respectively, such that the evaluation homomorphisms are continuous on \(A\) and \(B\). Then, every biseparating map \(T : A \to B\) is a weighted composition operator of the form \(Tf = h \cdot (f \circ \varphi)\), where \(\varphi\) is a homeomorphism from \(Y\) onto \(X\) and \(h\) is a nonvanishing element of \(B\). In particular, \(T\) is automatically continuous.