A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
Volume 119 / 1996
Studia Mathematica 119 (1996), 195-198
DOI: 10.4064/sm-119-2-195-198
Abstract
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].
