New Results on Idempotent Operators in Hilbert Spaces

New Results on Idempotent Operators in Hilbert Spaces

This paper provides a new proof of the operator norm identity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∥</mo><mi>Q</mi><mo>∥</mo><mo> </mo><mo&...

Full description

Saved in:
Bibliographic Details
Main Authors: Salma Aljawi, Cristian Conde, Kais Feki, Shigeru Furuichi
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Axioms
Subjects:
idempotent operators
operator norm
orthogonal projections
geometric proof
oblique projections
Online Access:https://www.mdpi.com/2075-1680/14/7/509
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper provides a new proof of the operator norm identity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∥</mo><mi>Q</mi><mo>∥</mo><mo> </mo><mo>=</mo><mo> </mo><mo>∥</mo><mi>I</mi><mo>−</mo><mi>Q</mi><mo>∥</mo></mrow></semantics></math></inline-formula>, where <i>Q</i> is a bounded idempotent operator on a complex Hilbert space, and <i>I</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.
ISSN:2075-1680

Similar Items