It implies that, for irreducible representations of C *-algebras, the only non-zero linear invariant subspace is the whole space.
2.
In the case of linear invariant systems, this is known as positive real transfer functions, and a fundamental tool is the so-called Kalman Yakubovich Popov lemma which relates the state space and the frequency domain properties of positive real systems.
3.
All linear invariant differential operators on homogeneous parabolic geometries, i . e . when " G " is semi-simple and " H " is a parabolic subgroup, are given dually by homomorphisms of generalized Verma modules.
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