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Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter

Authors
  • Novikov, A. A.1
  • Eskandarian, Z.1
  • 1 Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia , Kazan (Russia)
Type
Published Article
Journal
Russian Mathematics
Publisher
Allerton Press
Publication Date
Sep 28, 2016
Volume
60
Issue
10
Pages
67–71
Identifiers
DOI: 10.3103/S1066369X1610011X
Source
Springer Nature
Keywords
License
Yellow

Abstract

We prove that a measurable function f is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order unities fα and fβ with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities fα (α approaches to infinity) as a direct sum of one inductive and one projective limits. We also obtain some properties for the corresponding limit topologies.

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