A characterization of essential sets of function algebras

Jan Cerych

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


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.