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On an Algebraic Extension of $A(E)$
B. T. Batikyana, S. A. Grigoryanb a Institute of Mathematics, National Academy of Sciences of Armenia
b Kazan State University
Abstract:
An algebraic extension of the algebra $A(E)$, where $E$ is a compactum in $\mathbb C$ with nonempty connected interior, leads to a Banach algebra $B$ of functions that are holomorphic on some analytic set $K^\circ \subset \mathbb C^2$ 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.
Received: 09.02.1999 Revised: 12.02.2002
Citation:
B. T. Batikyan, S. A. Grigoryan, “On an Algebraic Extension of $A(E)$”, Mat. Zametki, 72:5 (2002), 649–653; Math. Notes, 72:5 (2002), 600–604
Linking options:
https://www.mathnet.ru/eng/mzm452https://doi.org/10.4213/mzm452 https://www.mathnet.ru/eng/mzm/v72/i5/p649
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Abstract page: | 339 | Full-text PDF : | 166 | References: | 47 | First page: | 2 |
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