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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References
L. Asimow and A. J. Ellis, Convexity Theory and its Applications in Functional Analysis (Academic, London, 1980).
L. V. Kantorovich and G. P. Akilov, Functional Analysis (Nauka, Moscow, 1984) [in Russian].
G. Kothe, Topological Vector Spaces I (Springer, New York, 1969).
A. Novikov, “L 1-space for a positive operator affiliated with von Neumann algebra,” Positivity 21, 359–375 (2017).
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).
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(Submitted by F. G. Avkhadiev)
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Eskandarian, Z. Locally Convex Limit Spaces of Measurable Functions with Order Units and Its Duals. Lobachevskii J Math 39, 195–199 (2018). https://doi.org/10.1134/S1995080218020105
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DOI: https://doi.org/10.1134/S1995080218020105