  We derive several entanglement conditions employing non-hermitian operators.
We start with two conditions that were derived previously for field mode
operators, and use them to derive conditions that can be used to show the
existence of field-atom entanglement and entanglement between groups of atoms.
The original conditions can be strengthened by making them invariant under
certain sets of local unitary transformations, such as Gaussian operations. We
then apply these conditions to several examples, such as the Dicke model. We
conclude with a short discussion of how local uncertainty relations with
non-hermitian operators can be used to derive entanglement conditions.
