Lateral continuity and orthogonally additive operators

Array

Authors

  • A.I. Gumenchuk Chernivtsi Medical College, 60 Geroiv Maidanu str., 58001, Chernivtsi, Ukraine

DOI:

https://doi.org/10.15330/cmp.7.1.49-56

Keywords:

orthogonally additive operator, lateral continuity

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).

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Published

2015-07-03

How to Cite

(1)
Gumenchuk, A. Lateral Continuity and Orthogonally Additive Operators: Array. Carpathian Math. Publ. 2015, 7, 49-56.

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Section

Scientific articles