Abstract
In this paper, a characterization of continuous module homomorphisms on random semi-normed modules is first given; then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules.
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The first author of this paper is supported in part by the Foundation for University Key Teachers of the Ministry of Education of China, the National Natural Science Foundation of China (No. 10071063) and the Natural Science Foundation of Fujian Province of China (F99027).
Erratum: GRANVILLE Andrew (Department of Mathematics, University of Geogia, Athens, GA30602, USA) is not an author of the following paper: On the Residues of Binomial Coefficients and Their Products Modulo Prime Powers, Acta Mathematica Sinica (English Series), 18(2), 277–288 (2002)
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Guo, T.X., Zhu, L.H. A Characterization of Continuous Module Homomorphisms on Random Semi-Normed Modules and Its Applications. Acta Math Sinica 19, 201–208 (2003). https://doi.org/10.1007/s10114-002-0210-x
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DOI: https://doi.org/10.1007/s10114-002-0210-x