Locally Convex Limit Spaces of Measurable Functions with Order Units and Its Duals
- Authors: Eskandarian Z.1
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Affiliations:
- Kazan (Volga Region) Federal University
- Issue: Vol 39, No 2 (2018)
- Pages: 195-199
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201370
- DOI: https://doi.org/10.1134/S1995080218020105
- ID: 201370
Cite item
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.
About the authors
Zohreh Eskandarian
Kazan (Volga Region) Federal University
Author for correspondence.
Email: zohreh.eskandarian@gmail.com
Russian Federation, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008