Lateral continuity and orthogonally additive operators

A. I. Gumenchuk

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).

Keywords


orthogonally additive operator, lateral continuity

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