A Maximal Algebra.
A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
A note on minimal envelopes of Douglas algebras, minimal support sets, and restricted Douglas algebras.
A semitopological algebra without proper closed subalgebras
To Czesław Ryll-Nardzewski on his 70th birthday
A theorem concerning Ditkin's condition
Algèbres de fonctions analytiques dans le disque
An upper bound for the distance to finitely generated ideals in Douglas algebras
Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.
Associative and Lie subalgebras of finite codimension