New Results on Idempotent Operators in Hilbert Spaces
This paper provides a new proof of the operator norm identity ∥Q∥ = ∥I−Q∥, where Q is a bounded idempotent operator on a complex Hilbert space, and I is the identity operator. We also derive explicit lower and upper bounds for the distance from an arbitrary idempotent operator to the set of orthogonal projections. Our approach simplifies existing proofs.
Authors
- Kais Feki (ORCID: https://orcid.org/0000-0002-9326-4173)
- Cristian Conde
- Shigeru Furuichi (ORCID: https://orcid.org/0000-0002-9929-0954)
- Salma Aljawi (ORCID: https://orcid.org/0000-0001-7928-5624)
Institutions
- Nihon University (JP)
- Princess Nourah bint Abdulrahman University (SA)
- Consejo Nacional de Investigaciones Científicas y Técnicas (AR)
- National University of General Sarmiento (AR)
- Najran University (SA)
- Saveetha University (IN)
Publication Details
- Journal
- Axioms
- Published
- 2025-06-30
- DOI
- https://doi.org/10.3390/axioms14070509
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00