Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures.
Dito Bishop nagtrabaho sa unipormeng algebras (commutative Banach algebras sa produkto na ang mga norms ang mga multo norms) proving resulta tulad ng antisymmetric agnas ng isang unipormeng algebra, ang Bishop-DeLeeuw teorama, at ang katibayan ng pagkakaroon ng Jensen hakbang.