2013
DOI: 10.1016/j.jfa.2013.05.035
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Function algebras with a strongly precompact unit ball

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 L 2 (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 pre… Show more

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