Polynomially peripheral range-preserving maps between Banach algebras |
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Authors: | M Najafi Tavani |
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Institution: | 1.Department of Mathematics,Islamshahr Branch, Islamic Azad University,Islamshahr,Islamic Republic of Iran |
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Abstract: | Let A and B be two Banach function algebras and p a two variable polynomial \(p(z,w)=zw+az+bw+c\), (\(a,b,c\in {\mathbb {C}}\)). We characterize the general form of a surjection \(T: A \longrightarrow B\) which satisfies \(\mathrm{Ran}_\pi (p(Tf,Tg))\cap \mathrm{Ran}_\pi (p(f,g))\ne \emptyset , (f,g\in A\) and \(c\ne ab)\), where \(\mathrm{Ran}_\pi (f)\) is the peripheral range of f. |
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