Idempotent linear relations

ARIAS, M. LAURA; CONTINO, MAXIMILIANO; MAESTRIPIERI, ALEJANDRA; MARCANTOGNINI, STEFANIA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2022 vol. 516

0022-247X

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.