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

Authors
  • Eskandarian, Zohreh1
  • 1 Kazan (Volga Region) Federal University, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008, Russia , Kazan, Tatarstan (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Mar 21, 2018
Volume
39
Issue
2
Pages
195–199
Identifiers
DOI: 10.1134/S1995080218020105
Source
Springer Nature
Keywords
License
Yellow

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.

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