Idempotent linear relations - Arias, Maria Laura (2022)
A linear relation E acting on a Hilbert space is idempotent if E2=E. A triplet of subspaces is needed to characterize a given idempotent: (ranE,ran(I−E),domE), or equivalently, (ker⁡(I−E),ker⁡E,mulE). The relations satisfying the inclusions E2⊆E (sub-idempotent) or E⊆E2 (super-idempotent) play an important role. Lastly, the adjoint and the closure of an idempotent linear relation are studied.