Range transformations on a Banach function algebra
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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 $\S 2$ 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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 297 (1986), 629-643
- MSC: Primary 46J10; Secondary 46H30
- DOI: https://doi.org/10.1090/S0002-9947-1986-0854089-3
- MathSciNet review: 854089