Extensions of orthogonally additive operators

A. V. Gumenchuk, M. A. Pliev, M. M. Popov
Chernivtsi Medical College, Chernivtsi National University
We find natural sufficient conditions on a subset $D$ of a vector lattice $E$ under which every orthogonally additive operator $T_0\colon D \to X$, where $X$ is a vector space, can be extended to an orthogonally additive operator $T\colon E \to X$. Two theorems on the extension from lateral ideals and lateral bands, respectively, are obtained.
vector lattice; orthogonally additive operator; disjointness preserving operator
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