English

Idempotent linear relations

Functional Analysis 2022-04-08 v1

Abstract

A linear relation EE acting on a Hilbert space is idempotent if E2=E.E^2=E. A triplet of subspaces is needed to characterize a given idempotent: (ranE,ran(IE),domE),(\mathrm{ran} \, E, \mathrm{ran}(I-E), \mathrm{dom}\, E), or equivalently, (ker(IE),kerE,mulE).(\mathrm{ker}(I-E), \mathrm{ker}\, E, \mathrm{mul} \, E). The relations satisfying the inclusions E2EE^2 \subseteq E (sub-idempotent) or EE2E \subseteq E^2 (super-idempotent) play an important role. Lastly, the adjoint and the closure of an idempotent linear relation are studied.

Cite

@article{arxiv.2204.03581,
  title  = {Idempotent linear relations},
  author = {Maria Laura Arias and Maximiliano Contino and Alejandra Maestripieri and Stefania Marcantognini},
  journal= {arXiv preprint arXiv:2204.03581},
  year   = {2022}
}
R2 v1 2026-06-24T10:41:28.558Z