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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Range transformations on a Banach function algebra

Author: Osamu Hatori
Journal: Trans. Amer. Math. Soc. 297 (1986), 629-643
MSC: Primary 46J10; Secondary 46H30
MathSciNet review: 854089
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Abstract: We study the range transformations $ \operatorname{Op} ({A_{D,}}\operatorname{Re} B)$ and $ \operatorname{Op} ({A_D},B)$ for Banach function algebras $ A$ and $ B$. As a special instance, the harmonicity of functions in $ \operatorname{Op} ({A_D},\operatorname{Re} A)$ for a nontrivial function algebra $ A$ is established and is compared with previous investigations of $ \operatorname{Op} ({A_D},A)$ and $ \operatorname{Op} ({(\operatorname{Re} A)_I},(\operatorname{Re} A))$ for an interval $ I$. In $ \S2$ we present some results on $ \operatorname{Op} ({A_D},B)$ and use them to show that functions in $ {\operatorname{Op} ^C}({A_D},B)$ are analytic for certain Banach function algebras.

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Keywords: Function algebra, Banach function algebra, range transformation, ultraseparating
Article copyright: © Copyright 1986 American Mathematical Society