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Spectral sets and distinguished varieties in the symmetrized bidisc.
- Source :
-
Journal of Functional Analysis . May2014, Vol. 266 Issue 9, p5779-5800. 22p. - Publication Year :
- 2014
-
Abstract
- Abstract: We show that for every pair of matrices , having the closed symmetrized bidisc Γ as a spectral set, there is a one dimensional complex algebraic variety Λ in Γ such that for every matrix valued polynomial , The variety Λ is shown to have the determinantal representation where F is the unique matrix of numerical radius not greater than 1 that satisfies When is a strict Γ-contraction, then Λ is a distinguished variety in the symmetrized bidisc, i.e. a one dimensional algebraic variety that exits the symmetrized bidisc through its distinguished boundary. We characterize all distinguished varieties of the symmetrized bidisc by a determinantal representation as above. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 266
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 95316716
- Full Text :
- https://doi.org/10.1016/j.jfa.2013.12.022