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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Regularity and Algebras of Analytic Functions in Infinite Dimensions


Authors: R. M. Aron, P. Galindo, D. García and M. Maestre
Journal: Trans. Amer. Math. Soc. 348 (1996), 543-559
MSC (1991): Primary 46G20; Secondary 46J10
MathSciNet review: 1340167
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Abstract: A Banach space $E$ is known to be Arens regular if every continuous linear mapping from $E$ to $E^{\prime}$ 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 $M_b(U)$.


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Additional Information

R. M. Aron
Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44242
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

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01553-X
PII: S 0002-9947(96)01553-X
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
Article copyright: © Copyright 1996 American Mathematical Society