Idempotent linear relations

2022/04/07 by Arias, Maria Laura, Contino, Maximiliano, Maestripieri, Alejandra +1
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2204.03581

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 ⊆ 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.

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