Maps between Banach function algebras satisfying certain norm conditions

• Autorzy: Maliheh Hosseini , Fereshteh Sady
• Języki publikacji: EN

Abstrakty

EN

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y, respectively, and let \(\bar A\) and \(\bar B\) be their uniform closures. Let I, I′ be arbitrary non-empty sets, α ∈ ℂ\{0}, ρ: I → A, τ: l′ → a and S: I → B T: l′ → B be maps such that ρ(I, τ(I′) and S(I), T(I′) are closed under multiplications and contain exp A and expB, respectively. We show that if ‖S(p)T(p′)−α‖Y=‖ρ(p)τ(p′) − α‖x for all p ∈ I and p′ ∈ I′, then there exist a real algebra isomorphism S: A → B, a clopen subset K of M B and a homeomorphism ϕ: M B → M A between the maximal ideal spaces of B and A such that for all f ∈ A, [...] where \(\hat \cdot\) denotes the Gelfand transformation. Moreover, S can be extended to a real algebra isomorphism from \(\bar A\) onto \(\bar B\) inducing a homeomorphism between \(M_{\bar B}\) and \(M_{\bar A}\) . We also show that under an additional assumption related to the peripheral range, S is complex linear, that is A and B are algebraically isomorphic. We also consider the case where α = 0 and X and Y are locally compact.

Słowa kluczowe

EN

Banach function algebras; Uniform algebras; Norm-preserving; Peripheral range; Choquet boundary

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: 2013
• Tom: 11
• Numer: 6
• Strony: 1020-1033

Daty

wydano

2013-06-01

online

2013-03-28

Twórcy

autor

Maliheh Hosseini

• Department of Mathematics, K.N. Toosi University of Technology, 16315-1618, Tehran, Iran

autor

Fereshteh Sady

• Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134, Tehran, Iran

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0224-x