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

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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 f α and f β with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities f α (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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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    A. A. Novikov & Z. Eskandarian

Authors
  1. A. A. Novikov
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  2. Z. Eskandarian
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Correspondence to A. A. Novikov.

Additional information

Original Russian Text © A.A. Novikov, Z. Eskandarian, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 10, pp. 80–85.

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Novikov, A.A., Eskandarian, Z. Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter. Russ Math. 60, 67–71 (2016). https://doi.org/10.3103/S1066369X1610011X

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  • DOI: https://doi.org/10.3103/S1066369X1610011X

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