Lateral continuity and orthogonally additive operators
Journal Title: Карпатські математичні публікації - Year 2015, Vol 7, Issue 1
Abstract
We generalize the notion of a laterally convergent net from increasing nets to general ones and study the corresponding lateral continuity of maps. The main result asserts that, the lateral continuity of an orthogonally additive operator is equivalent to its continuity at zero. This theorem holds for operators that send laterally convergent nets to any type convergent nets (laterally, order or norm convergent).
Authors and Affiliations
A. Gumenchuk
Keywords
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- EP ID EP538619
- DOI 10.15330/cmp.7.1.49-56
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