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Topological algebras with pseudoconvexly bounded elements. (English) Zbl 1091.46026
Jarosz, Krzysztof (ed.) et al., Topological algebras, their applications, and related topics. Proceedings of the conference to celebrate the 70th birthday of Professor Wiesław Żelazko, Bȩdlewo, Poland, May 11–17, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 67, 21-33 (2005).
Summary: 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.
For the entire collection see [Zbl 1063.46001].

MSC:
 46H05 General theory of topological algebras 46H20 Structure, classification of topological algebras