Generalizations of weakly peripherally multiplicative maps between uniform algebras

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Generalizations of Weakly Peripherally Multiplicative Maps Between Uniform Algebras

Let A and B be uniform algebras on first-countable, compact Hausdorff spaces X and Y , respectively. For f ∈ A, the peripheral spectrum of f , denoted by σπ(f) = {λ ∈ σ(f) : |λ| = ‖f‖}, is the set of spectral values of maximum modulus. A map T : A → B is weakly peripherally multiplicative if σπ(T (f)T (g)) ∩ σπ(fg) 6= ∅ for all f, g ∈ A. We show that if T is a surjective, weakly peripherally mu...

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Let X be a compact Hausdorff space; let τ : X → X be a topological involution; and let A ⊂ C(X, τ) be a real function algebra. Given an f ∈ A, the peripheral spectrum of f is the set σπ(f) of spectral values of f of maximum modulus. We demonstrate that if T1, T2 : A → B and S1, S2 : A → A are surjective mappings between real function algebras A ⊂ C(X, τ) and B ⊂ C(Y, φ) that satisfy σπ(T1(f)T2(...

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ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2011

ISSN: 0022-247X

DOI: 10.1016/j.jmaa.2010.08.051