Convergence theorems for pseudo-complete locally convex algebras (Q2248808)

The author studies bounded pseudo-complete locally convex algebras and inductive limits. He finds some sufficient conditions under which every bounded subset \(A\) is \(i\)-bounded, i.e., when there exists \(\lambda>0\) such that the smallest idempotent subset containing \(\lambda A\) is bounded. He also provides some necessary conditions under which a convergent sequence of elements of an algebra is locally convergent. Several examples from analysis are also considered.