Weak Sequential Completeness of Uniform Algebras

We prove that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional

A Peak Point Theorem for Uniform Algebras on Real-Analytic Varieties

It was once conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$, and if each point of $X$ is a peak point for $A$, then $A = C(X)$. This peak-point conjecture was disproved by Brian Cole in 1968. Here we establish a peak-point theorem for uniform algebras generated by real-analytic functions on real-analytic varieties, generalizing previous results of the authors and John Wermer

Uniform Approximation by Holomorphic and Harmonic Functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135501/1/jlms0129.pd