Norm conditions for real-algebra isomorphisms between uniform algebras

• Autorzy: Rumi Shindo
• Języki publikacji: EN

Abstrakty

EN

Let A and B be uniform algebras. Suppose that α ≠ 0 and A 1 ⊂ A. Let ρ, τ: A 1 → A and S, T: A 1 → B be mappings. Suppose that ρ(A 1), τ(A 1) and S(A 1), T(A 1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A 1, S(e 1)−1 ∈ S(A 1) and S(e 1) ∈ T(A 1) for some e 1 ∈ A 1 with ρ(e 1) = 1, then there exists a real-algebra isomorphism $$ \tilde S $$: A → B such that $$ \tilde S $$(ρ(f)) = S(e 1)−1 S(f) for every f ∈ A 1. We also give some applications of this result.

Słowa kluczowe

EN

Banach algebra; Uniform algebra; Norm-preserving

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 47B48: Operators on Banach algebras
• 46J10: Banach algebras of continuous functions, function algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 135-147

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Rumi Shindo

• Niigata University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0060-1