Extensions of orthogonally additive operators 

Author 
anna_hostyuk@ukr.net, misham.popov@gmail.com
Chernivtsi Medical College, Chernivtsi National University

Abstract 
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.

Keywords 
vector lattice; orthogonally additive operator; disjointness preserving operator

Reference 
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Pages 
214219

Volume 
41

Issue 
2

Year 
2014

Journal 
Matematychni Studii

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