Topological algebras with pseudoconvexly bounded elements
Volume 67 / 2005
Banach Center Publications 67 (2005), 21-33
MSC: Primary 46H05; Secondary 46H20.
DOI: 10.4064/bc67-0-2
Abstract
It is shown that every commutative sequentially bornologically complete Hausdorff algebra $A$ with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of $A$ is pseudoconvex. Several classes of topological algebras $A$ for which $r_A(a)\leq \beta_A(a)$ or $r_A(a)= \beta_A(a)$ for each $a\in A$ are described.
