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- W2053186711 abstract "Let A and B be two Banach function algebras on locally compact Hausdorff spaces X and Y , respectively. Let T be a multiplicatively range-preserving map from A onto B in the sense that ( T f T g ) ( Y ) = ( f g ) ( X ) for all f , g ∈ A . We define equivalence relations on appropriate subsets X ˜ and Y ˜ of X and Y , respectively, and show that T induces a homeomorphism between the quotient spaces of X ˜ and Y ˜ by these equivalence relations. In particular, if all points in the Choquet boundaries of A and B are strong boundary points, then X ˜ and Y ˜ are equal to the Choquet boundaries of A and B , respectively, and moreover, there exist a continuous function h on the Choquet boundary of B taking its values in { − 1 , 1 } and a homeomorphism φ from the Choquet boundary of B onto the Choquet boundary of A such that T f ( y ) = h ( y ) f ( φ ( y ) ) for all f ∈ A and y in the Choquet boundary of B . For certain Banach function algebras A and B on compact Hausdorff spaces X and Y , respectively, we can weaken the surjectivity assumption and give a representation for maps belonging 2-locally to the family of all multiplicatively range-preserving maps from A onto B ." @default.
- W2053186711 created "2016-06-24" @default.
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- W2053186711 date "2009-09-01" @default.
- W2053186711 modified "2023-09-24" @default.
- W2053186711 title "Multiplicatively range-preserving maps between Banach function algebras" @default.
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- W2053186711 doi "https://doi.org/10.1016/j.jmaa.2009.04.008" @default.
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