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Gutman A.E., Lisovskaya S.A.
The boundedness principle for lattice-normed spaces //
Sib. Math. J. 2009. V. 50, N 5. P. 830–837.
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, exact analogs of the theorems are proven for the case of lattice-normed spaces.

Keywords:Banach–Steinhaus theorem, Banach–Kantorovich space, cyclically compact set, Boolean valued analysis.
Type Article
Authors Gutman Alexander Efimovich
Lisovskaya Svetlana Alexeevna
Title The boundedness principle for lattice-normed spaces
Journal Siberian Mathematical Journal
Year 2009
Volume 50
Number 5
Pages 830–837
DOI 10.1007/s11202-009-0093-5
Language English
© 2009.06.03
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Project  Boolean-valued analysis 
Development of the theory of Boolean-valued models and their applications in functional analysis
 
 
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July 19, 2018