Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658348 | Topology and its Applications | 2015 | 15 Pages |
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 (1969) [12] 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) [5], is fixed.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
M.D. Mabula, S. Cobzaş,