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

DOI:
https://doi.org/10.1090/S0002-9947-96-01553-X

MathSciNet review:
1340167

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Abstract | References | Similar Articles | Additional Information

Abstract: A Banach space is known to be Arens regular if every continuous linear mapping from to is weakly compact. Let be an open subset of , and let denote the algebra of analytic functions on which are bounded on bounded subsets of lying at a positive distance from the boundary of We endow with the usual Fréchet topology. denotes the set of continuous homomorphisms . We study the relation between the Arens regularity of the space and the structure of .

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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:
https://doi.org/10.1090/S0002-9947-96-01553-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