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- W2013604292 abstract "Let $A$ and $B$ be Banach function algebras on compact Hausdorff spaces $X$ and $Y$, respectively. Given a non-zero scalar $alpha$and $s,tin Bbb N$ we characterize the general form of suitable powers of surjective maps $T, T': A longrightarrow B$ satisfying $|(Tf)^s (T'g)^t-alpha|_Y=|f^s g^t-alpha |_X$, for all $f,g in A$, where $|cdot |_X$ and $|cdot |_Y$ denote the supremum norms on $X$ and $Y$, respectively. A similar result is given for the case where $T=T'$ and $T$ is defined between certain subsets of $A$ and $B$. We also show that if $T: Alongrightarrow B$ is a surjective map satisfying the stronger condition$R_pi((Tf)^{s}(Tg)^{t}-alpha)cap R_pi(f^{s}g^{t}-alpha)neqvarnothing $ for all $f,g in A$, where $R_pi(cdot)$ denotes the peripheral range of the algebra elements, then there exists a homeomorphism $varphi$ from the Choquet boundary $c(B)$ of $B$ onto the Choquet boundary $c(A)$ of $A$ such that $(Tf)^{d}(y)=(T1)^{d}(y),(f circ varphi(y))^{d}$ for all $fin A$ and $yin c(B)$,where $d$ is the greatest common divisor of $s$ and $t$." @default.
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- W2013604292 date "2012-01-01" @default.
- W2013604292 modified "2023-09-26" @default.
- W2013604292 title "Banach function algebras and certain polynomially norm-preserving maps" @default.
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- W2013604292 doi "https://doi.org/10.15352/bjma/1342210157" @default.
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