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Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 195–199 | Cite as

Locally Convex Limit Spaces of Measurable Functions with Order Units and Its Duals

  • Zohreh Eskandarian
Article
  • 12 Downloads

Abstract

We consider linear normed spaces of measurable functions dominated by positive measurable function powered by real positive parameter. Also, we consider its dual and predual, and we propose a method for constructing a limit spaces of these functional spaces taken by power parameter. We prove that these limit spaces are (LF)-spaces and also prove that the limit spaces presume the relation of duality, i.e., the limit space of predual spaces is predual for the limit space of dominated functions, and the limit space of duals is dual for it. Also, the limit space of predual spaces is embedded into the limit space of dual spaces.

Keywords and phrases

inductive limit projective limit power parameter measurable function (LB)-space (LF)-space Frechet space locally convex space order unit base norm 

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    A. Novikov and Z. Eskandarian, “Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter,” Russ. Math. 60 (10), 67–71 (2016).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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