Let \({\mathcal{A}}\) and \({\mathcal{B}}\) be uniform algebras and p(z,w) = z^mwⁿ a twovariable monomial. We characterize maps T from certain subsets of \({\mathcal{A}}\) into \({\mathcal{B}}\) such that \(\sigma_{\pi}(p(T(f),T(g))) \subset \sigma_{\pi}(p(f,g))\) holds for all f and g in the domain of T; peripherally monomial-preserving maps. Furthermore \({\mathcal{A}}\) and \({\mathcal{B}}\) are proved to be isometrical isomorphic as Banach algebras. If the greatest common divisor of m and n is 1, then T is extended to an isometrical linear isomorphism; a weighted composition operator. An example of peripherally monomial-preserving surjections between uniform algebras which is not linear, nor multiplicative, nor injective is given when the greatest common divisor is strictly greater than 1.

中文翻译：

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均匀代数之间的周边保全映射

令\（{\ mathcal {A}} \）和\（{\ mathcal {B}} \}是统一代数，并且p（z，w）= z ^m w ⁿ是两个变量单项式。我们将映射\ T从\（{\ mathcal {A}} \）的某些子集刻画为\（{\ mathcal {B}} \\）到\（\ sigma _ {\ pi}（p（T（f），T （g）））\ subset \ sigma _ {\ pi}（p（f，g））\）适用于T域中的所有f和g；外围保留多项式的地图。此外\（{\ mathcal {A}} \）和\（{\ mathcal {B}} \\被证明是等距同构的，如Banach代数。如果m和n的最大公约数为1，则T扩展为等距线性同构；反之，加权合成运算符。当最大公除数严格大于1时，给出均匀代数之间的线性不保，非乘法，非内射的周边单项保界排斥的一个例子。