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The polynomial cluster value problem

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Prieto, Angeles and Ortega, Sofia (2018) The polynomial cluster value problem. Journal of mathematical analysis and applications, 461 (2). pp. 1459-1470. ISSN 0022-247X

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Official URL: https://doi.org/10.1016/j.jmaa.2018.01.055


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Abstract

The polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers. We prove several polynomial cluster value theorems for uniform algebras H(B) between A(u)(B) and H-infinity (B), where B is the open unit ball of a complex Banach space X. We also obtain new results about the original cluster value problem, especially for A(infinity) (B). Examples of spaces X considered here are spaces of continuous functions, l(1) and locally uniformly convex spaces. (C) 2018 Elsevier Inc. All rights reserved.


Item Type:Article
Uncontrolled Keywords:Álgebras de Banach, Álgebras uniformes
Palabras clave (otros idiomas):Strong peak point
Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Functional analysis and Operator theory
ID Code:46988
Deposited On:13 Feb 2019 12:51
Last Modified:19 Feb 2019 12:08

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