The Gleason-Kahane-Zelazko theorem and function algebras

Edoardo Vesentini

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Remarks on the bidual of Banach algebras (the $C^{*}$ case)

Bruno Iochum, Guy Loupias (1991)

Annales scientifiques de l'Université de Clermont. Mathématiques

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Real-linear isometries between function algebras

Takeshi Miura (2011)

Open Mathematics

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Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and $T (f) = κ \bar{f o φ}$ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not...