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On the corona theorem for almost periodic functions

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Abstract

LetAP +Σ (R n) denote the Banach algebra of all continuous almost periodic functions onR n whose Bohr-Fourier spectrum is contained in an additive semi-group Σ⊂[0, ∞)n. We show that the maximal ideal space ofAP +Σ (R n) may have a nonempty corona and we characterize all Σ for which the corona is empty. Analogous results are established for algebras of almost periodic functions with absolutely convergent Fourier series.

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  1. Fakultät für Mathematik, TU Chemnitz, D-09107, Chemnitz, Germany

    A. Böttcher

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  1. A. Böttcher
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Böttcher, A. On the corona theorem for almost periodic functions. Integr equ oper theory 33, 253–272 (1999). https://doi.org/10.1007/BF01230734

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  • DOI: https://doi.org/10.1007/BF01230734

MSC 1991

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