Biseparating Maps on Fréchet Function Algebras

Abstract EN

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→B is a weighted composition operator of the form Tf=h·(f∘φ), where φ is a homeomorphism from Y onto X and h is a nonvanishing element of B.

In particular, T is automatically continuous.