Idempotent linear relations
Abstract
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: (ran \, E, ran(I-E), dom\, E), or equivalently, (ker(I-E), ker\, E, mul \, E). The relations satisfying the inclusions E2 ⊂eq E (sub-idempotent) or E ⊂eq E2 (super-idempotent) play an important role. Lastly, the adjoint and the closure of an idempotent linear relation are studied.
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