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Matematicheskie Zametki, 2002, Volume 72, Issue 5, Pages 649–653
DOI: https://doi.org/10.4213/mzm452
(Mi mzm452)
 

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
References:
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
English version:
Mathematical Notes, 2002, Volume 72, Issue 5, Pages 600–604
DOI: https://doi.org/10.1023/A:1021492519114
Bibliographic databases:
UDC: 517.986
Language: Russian
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
Citation in format AMSBIB
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