A characterization of essential sets of function algebras

Jan Cerych

Address.
 Charles Univerity in Prague, Faculty of Mathematics and Physics, Sokolovska  83, 186 00 Praha 8, Czech Republic
 

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Abstract.
In the present note, we characterize the essential set $E$ of a function algebra $A$ defined on a compact Hausdorff space $X$ in terms of local properties of functions in $A$ at the points off $E$.

AMSclassification. 46J10.

Keywords.  Compact Hausdorff space $X$, the sup-norm algebra $C(X)$ of all complex-valued continuous f`unctions on $X$, its closed subalgebras (called function algebras), measure orthogonal to a function algebra.