Article
Function algebras with a strongly precompact unit ball
Author/s | Lacruz Martín, Miguel Benito
Rodríguez Piazza, Luis |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2013-10-01 |
Deposit Date | 2016-07-12 |
Published in |
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Abstract | Let µ be a finite positive Borel measure with compact support K ⊆ C, and regard L∞(µ) as an algebra of multiplication operators on the Hilbert space L2(µ). Then consider the subalgebra A(K) of all continuous functions on ... Let µ be a finite positive Borel measure with compact support K ⊆ C, and regard L∞(µ) as an algebra of multiplication operators on the Hilbert space L2(µ). Then consider the subalgebra A(K) of all continuous functions on K that are analytic on the interior of K, and the subalgebra R(K) defined as the uniform closure of the rational functions with poles outside K. Froelich and Marsalli showed that if the restriction of the measure µ to the boundary of K is discrete then the unit ball of A(K) is strongly precompact, and that if the unit ball of R(K) is strongly precompact then the restriction of the measure µ to the boundary of each component of C\K is discrete. The aim of this paper is to provide three examples that go to clarify the results of Froelich and Marsalli; in particular, it is shown that the converses to both statements are false. |
Funding agencies | Ministerio de Educación, Cultura y Deporte (MECD). España Junta de Andalucía |
Project ID. | MTM 2012-30748
FQM-3737 P09-FQM-4745 |
Citation | Lacruz Martín, M.B. y Rodríguez Piazza, L. (2013). Function algebras with a strongly precompact unit ball. Journal of Functional Analysis, 265 (7), 1357-1366. |
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