Abstract
An algebraic extension of the algebra A(E), where E is a compactum in ℂ with nonempty connected interior, leads to a Banach algebra B of functions that are holomorphic on some analytic set Ko⊂ ℂ2 with boundary bK and continuous up to bK. The singular points of the spectrum of B and their defects are investigated. For the case in which B is a uniform algebra, the depth of B in the algebra C(bK) is estimated. In particular, conditions under which B is maximal on bK are obtained.
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Batikyan, B.T., Grigoryan, S.A. On an Algebraic Extension of A(E) . Mathematical Notes 72, 600–604 (2002). https://doi.org/10.1023/A:1021492519114
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DOI: https://doi.org/10.1023/A:1021492519114