Weighted composition operators and the Gleason-Kahane-Zelazko theorem

The main purpose of this paper is to investigate extensions of the Banach-Stone theorem and of the Holsztynski theorem to some locally multiplicatively convex associative algebras. The proofs are based on a generalization of a theorem, due to A. Gleason, J.-P. Kahane and W. Zelazko, characterizing continuous characters of a unital associative Banach algebra among all its linear forms.