Open AccessLateral continuity and orthogonally additive operators
Author(s) -
A. I. Gumenchuk
Publication year - 2015
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.7.1.49-56
Subject(s) - mathematics , operator (biology) , norm (philosophy) , pure mathematics , order (exchange) , zero (linguistics) , net (polyhedron) , operator norm , discrete mathematics , operator theory , geometry , biochemistry , chemistry , linguistics , philosophy , finance , repressor , political science , transcription factor , law , economics , gene
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).