## Regularity and Algebras of Analytic Functions in Infinite Dimensions

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- by R. M. Aron, P. Galindo, D. García and M. Maestre PDF
- Trans. Amer. Math. Soc.
**348**(1996), 543-559 Request permission

## Abstract:

A Banach space $E$ is known to be Arens regular if every continuous linear mapping from $E$ to $E’$ is weakly compact. Let $U$ be an open subset of $E$, and let $H_b(U)$ denote the algebra of analytic functions on $U$ which are bounded on bounded subsets of $U$ lying at a positive distance from the boundary of $U.$ We endow $H_b(U)$ with the usual Fréchet topology. $M_b(U)$ denotes the set of continuous homomorphisms $\phi :H_b(U) \to \mathbb {C}$. We study the relation between the Arens regularity of the space $E$ and the structure of $M_b(U)$.## References

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## Additional Information

**R. M. Aron**- Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
- MR Author ID: 27325
- Email: aron@mcs.kent.edu
**P. Galindo**- Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain
- Email: galindo@vm.ci.uv.es
**D. García**- Email: garciad@vm.ci.uv.es
**M. Maestre**- Email: maestre@vm.ci.uv.es
- Received by editor(s): May 9, 1994
- Additional Notes: The first author was supported in part by US–Spain Joint Committee for Cultural and Educational Cooperation, grant II–C 91024, and by NSF Grant Int-9023951

Supported in part by DGICYT pr. 91-0326 and by grant 93-081; the research of the second author was undertaken in part during the academic year 1993-94 while visiting Kent State University

The third author supported in part by DGICYT pr. 91-0326

The fourth author supported in part by US–Spain Joint Committee for Cultural and Educational Cooperation, grant II–C 91024 and by DGICYT pr. P.B.91-0326 and P.B.91-0538 - © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 543-559 - MSC (1991): Primary 46G20; Secondary 46J10
- DOI: https://doi.org/10.1090/S0002-9947-96-01553-X
- MathSciNet review: 1340167