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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $M_b(U)$.
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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