Zabrejko's lemma and the fundamental principles of functional analysis in the asymmetric case

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Authors

Mabula, Mokhwetha Daniel
Cobzas, Stefan

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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.

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Keywords

Asymmetric normed space, Uniform boundedness principle, Open mapping theorem, Closed graph theorem, Baire category, Bitopological space

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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.