The numerical range and the spectrum of a product of two orthogonal projections
| Autor: | Hubert Klaja |
|---|---|
| Přispěvatelé: | Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP) |
| Rok vydání: | 2014 |
| Předmět: |
Convex hull
orthogonal projections annihilating pair 47A12 47A10 Closure (topology) 010103 numerical & computational mathematics [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences symbols.namesake uncertainty principle FOS: Mathematics 0101 mathematics Numerical range Eigenvalues and eigenvectors Mathematics method of alternating projections Applied Mathematics Friedrich angle 010102 general mathematics Mathematical analysis Spectrum (functional analysis) Hilbert space Linear subspace Functional Analysis (math.FA) Mathematics - Functional Analysis Rate of convergence symbols Analysis |
| Zdroj: | Journal of Mathematical Analysis and Applications. 411:177-195 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2013.09.024 |
| Popis: | 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. Comment: 25 Pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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