Title :

The numerical range and the spectrum of a product of two orthogonal projections

Author(s) :

Klaja, Hubert [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

annihilating pair
Numerical range
orthogonal projections
Friedrich angle
method of alternating projections
uncertainty principle
annihilating pair.

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

The aim of this paper is to describe the closure of the numerical range of the product of two orthogonal projections in Hilbert space as a closed convex hull of some explicit ellipses parametrized by points in the spectrum. ...
Show more >The aim of this paper is to describe the closure of the numerical range of the product of two orthogonal projections in Hilbert space as a closed convex hull of some explicit ellipses parametrized by points in the spectrum. Several improvements (removing the closure of the numerical range of the operator, using a parametrization after its eigenvalues) are possible under additional assumptions. An estimate of the least angular opening of a sector with vertex $1$ containing the numerical range of a product of two orthogonal projections onto two subspaces is given in terms of the cosine of the Friedrichs angle. Applications to the rate of convergence in the method of alternating projections and to the uncertainty principle in harmonic analysis are also discussed.Show less >

Language :

Anglais

Comment :

25 Pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T10:11:38Z