Resumen de Weakly-peripherally multiplicative conditions and isomorphisms between uniform algebras

Rumi Shindo

• Suppose that A and B are uniform algebras on compact Hausdorff spaces X and Y , respectively. Let ;  : ¥Ë ¡æ A and S; T : ¥Ë ¡æ B be mappings on a nonempty set ¥Ë. Suppose that (¥Ë); (¥Ë) and S(¥Ë); T(¥Ë) are closed under multiplications and contain expA and expB respectively and that S(e1) ¡ô S(¥Ë)..1, T(e2) ¡ô T(¥Ë)..1 with |S(e1)T(e2)| = 1 on Ch(B) for some fixed e1; e2 ¡ô A1 with (e1) =  (e2) = 1. If  (S(f)T(g)) ¡û  ((f) (g)) .= . for all f; g ¡ô ¥Ë and there exists a first-countable dense subset DB in Ch(B), or a first-countable dense subset DA in Ch(A), then there exists an algebra isomorphism eS : A ¡æ B such that eS((f)) = S(e1)..1S(f) and eS( (f)) = T(e2)..1T(f) for every f ¡ô ¥Ë.