# Norm conditions for real-algebra isomorphisms between uniform algebras

Open Mathematics (2010)

- Volume: 8, Issue: 1, page 135-147
- ISSN: 2391-5455

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topRumi Shindo. "Norm conditions for real-algebra isomorphisms between uniform algebras." Open Mathematics 8.1 (2010): 135-147. <http://eudml.org/doc/269806>.

@article{RumiShindo2010,

abstract = {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.},

author = {Rumi Shindo},

journal = {Open Mathematics},

keywords = {Banach algebra; Uniform algebra; Norm-preserving; uniform algebra; isomorphisms; norm preserving},

language = {eng},

number = {1},

pages = {135-147},

title = {Norm conditions for real-algebra isomorphisms between uniform algebras},

url = {http://eudml.org/doc/269806},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Rumi Shindo

TI - Norm conditions for real-algebra isomorphisms between uniform algebras

JO - Open Mathematics

PY - 2010

VL - 8

IS - 1

SP - 135

EP - 147

AB - 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.

LA - eng

KW - Banach algebra; Uniform algebra; Norm-preserving; uniform algebra; isomorphisms; norm preserving

UR - http://eudml.org/doc/269806

ER -

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