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Aug 2, 2020 at 9:10 comment added András Bátkai Simon refers to this explicitly in "An abstract Kato inequality...", on page 1068 just after the Definition.
Jun 19, 2020 at 12:57 comment added MaoWao Simon has the unfortunate habit of sometimes writing something like $(u,A u)$, when he means $q_A(u,u)$, where $q_A$ is the quadratic form associated with $A$. In any case, Ouhabaz' article "Invariance of Closed Convex Sets and Domination Criteria for Semigroups" seems to be the better source for domination of semigroups - for example, he gives characterization purely in terms of the quadratic forms where Simon has form and operator domains.
Jun 19, 2020 at 10:12 history asked Alex M. CC BY-SA 4.0