Zabrejko's lemma and the fundamental principles of functional analysis in the asymmetric case
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Date
Authors
Mabula, Mokhwetha Daniel
Cobzas, Stefan
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Some versions of the fundamental principles of the functional analysis in asymmetric
normed spaces – the Open Mapping Theorem, the Closed Graph Theorem and
the Uniform Boundedness Principle – are proved. The proofs are based on an
asymmetric version of a lemma of Zabreijko on the continuity of the
countably subadditive functionals. At the same time a flaw in the proof of the
Uniform Boundedness Principle, given in the book by Cobzaş (2013), is fixed.
Description
Keywords
Asymmetric normed space, Uniform boundedness principle, Open mapping theorem, Closed graph theorem, Baire category, Bitopological space
Sustainable Development Goals
Citation
Mabula, MD & Cobzas, S 2015, 'Zabrejko's lemma and the fundamental principles of functional analysis in the asymmetric case', Topology and its Applications, vol. 184, pp. 1-15.