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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 5, Pages 1050–1059 (Mi smj2029)  
This article is cited in 4 scientific papers (total in 4 papers)

The boundedness principle for lattice-normed spaces

A. E. Gutmana, S. A. Lisovskayab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
Full-text PDF (349 kB) Citations (4)
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Abstract: The three classical facts of the theory of normed spaces are considered: the boundedness principle, the Banach–Steinhaus theorem, and the uniform boundedness principle for a compact convex set. By means of Boolean valued analysis, the analogs of the theorems are proven in a lattice-normed space setting.
Keywords: Banach–Steinhaus theorem, Banach–Kantorovich space, cyclically compact set, Boolean valued analysis.
Received: 02.06.2009
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 5, Pages 830–837
DOI: https://doi.org/10.1007/s11202-009-0093-5
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: A. E. Gutman, S. A. Lisovskaya, “The boundedness principle for lattice-normed spaces”, Sibirsk. Mat. Zh., 50:5 (2009), 1050–1059; Siberian Math. J., 50:5 (2009), 830–837
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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