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 : A → B such that (ρ(f)) = S(e 1)−1 S(f) for every f ∈ A 1. We also give some applications of this result.
@article{bwmeta1.element.doi-10_2478_s11533-009-0060-1,
author = {Rumi Shindo},
title = {Norm conditions for real-algebra isomorphisms between uniform algebras},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {135-147},
zbl = {1201.47039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0060-1}
}
Rumi Shindo. Norm conditions for real-algebra isomorphisms between uniform algebras. Open Mathematics, Tome 8 (2010) pp. 135-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0060-1/
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