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Regular variation, tological dynamics, and the uniform boundedness theorem

Ostaszewski, Adam (2010) Regular variation, tological dynamics, and the uniform boundedness theorem. Topology Proceedings, 36. pp. 305-336. ISSN 0146-4124

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In the metrizable topological groups context, a semi-direct product construction provides a canonical multiplicative representation for arbitrary continuous flows. This implies, modulo metric differences, the topological equivalence of the natural flow formalization of regular variation of N. H. Bingham and A. J. Ostaszewski in [Topological regular variation: I. Slow variation, [to appear in Topology and its Applications]with the B. Bajsanski and J. Karamata group formulation in [Regularly varying functions and the principle of egui-continuity, Publ. Ramanujan Inst. 1 (1968/1969), 235-246]. In consequence, topological theorems concerning subgroup actions may be lifted to the flow setting. Thus, the Bajsanski-Karamata Uniform Boundedness Theorem (UBT), as it applies to cocycles in the continuous and Baire cases, may be reformulated and refined to hold under Baire-style Caratheodory conditions. Its connection to the classical UBT, due to Stefan Banach and Hugo Steinhaus, is clarified. An application to Banach algebras is given.

Item Type: Article
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Additional Information: © 2010 Topology Proceedings
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 10 Jun 2011 15:39
Last Modified: 11 Oct 2021 23:10

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