Regularity of $R(X)$ does not pass to finite unions
We show that there are compact plane sets $X$, $Y$ such that $R(X)$ and $R(Y)$ are regular but $R(X \cup Y)$ is not regular.
math.FA↗
arXiv subjects
Joel Feinstein
Publications and source records attributed to Joel Feinstein.
Partial regularity and t-analytic sets for Banach function algebras
In this note we introduce the notion of $t$-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling's conjecture in $H^\infty$. A description of all closed $t$-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in Daoui et al. (Proc. Am. Math. Soc. 131:3211-3220, 2003) concerning the $O$-analyticity and $S$-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular.
math.FA↗