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Dual characterization of absolutely representing systems in inductive limits of Banach spaces

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Abstract

We establish a dual criterion for absolutely representing systems in the spaces of a sufficiently broad class of inductive limits of sequences of Banach spaces. The result is stated without any additional restrictions on the system. We consider applications to the systems of partial fractions in the spaces of locally analytic functions.

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Authors and Affiliations

  1. National Research Nuclear University “MEPhI”, Moscow, Russia

    V. B. Sherstyukov

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  1. V. B. Sherstyukov
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Correspondence to V. B. Sherstyukov.

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Original Russian Text Copyright © 2010 Sherstyukov V. B.

The author was supported by the Russian Federal Agency for Education (Grant 2.1.1/6827) and the Ministry for Education of the Russian Federation (Grants 268, 795, and 943).

Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 930–943, July–August, 2010.

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Sherstyukov, V.B. Dual characterization of absolutely representing systems in inductive limits of Banach spaces. Sib Math J 51, 745–754 (2010). https://doi.org/10.1007/s11202-010-0075-7

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  • DOI: https://doi.org/10.1007/s11202-010-0075-7

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