Skip to main content
Article thumbnail
Location of Repository

Regular variation, tological dynamics, and the uniform boundedness theorem

By Adam Ostaszewski

Abstract

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

Topics: QA Mathematics
Publisher: Department of Mathematics, Auburn University, Alabama
Year: 2010
OAI identifier: oai:eprints.lse.ac.uk:35910
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://topology.auburn.edu/tp/ (external link)
  • http://eprints.lse.ac.uk/35910... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.