On C-compact orthogonally additive operators

Abstract

We consider C-compact orthogonally additive operators in vector lattices. After providing some examples of C-compact orthogonally additive operators on a vector lattice with values in a Banach space we show that the set of those operators is a projection band in the Dedekind complete vector lattice of all regular orthogonally additive operators. In the second part of the article we introduce a new class of vector lattices, called C-complete, and show that any laterally-to-norm continuous C-compact orthogonally additive operator from a C-complete vector lattice to a Banach space is narrow, which generalizes a result of Pliev and Popov.