Weighted composition operators and the Gleason?Kahane?Zelazko theorem

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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.