Transactions of the American Mathematical Society

Author(s): R. M. Aron; P. Galindo; D. García; M. Maestre
Journal: Trans. Amer. Math. Soc. 348 (1996), 543-559.
MSC (1991): Primary 46G20; Secondary 46J10
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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

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

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46G20, 46J10

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

M. Maestre
Email: maestre@vm.ci.uv.es

DOI: 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
Copyright of article: Copyright 1996, American Mathematical Society

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