Real-linear isometries between function algebras

• Autorzy: Takeshi Miura
• Języki publikacji: EN

Abstrakty

EN

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 $T\left( f \right) = \kappa \overline {fo\phi }$ on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.

Słowa kluczowe

EN

Commutative Banach algebra; Function algebra; Isometry; Isomorphism; Uniform algebra

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 778-788

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Takeshi Miura

• Yamagata University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0044-9