  In this article, we study questions of uniqueness of form extension for
certain magnetic Schr\"odinger forms. The method is based on the theory of
ordered Hilbert spaces and the concept of domination of semigroups. We review
this concept in an abstract setting and give a characterization in terms of the
associated forms. Then we use it to prove a theorem that transfers uniqueness
of form extension of a dominating form to that of a dominated form. This result
is applied in two concrete situations: magnetic Schr\"odinger forms on graphs
and on domains in Euclidean space.

Functional Analysis