Author:
Farenick D. R.,Browne Patrick J.
Abstract
SynopsisLet Aij, l≦j≦k, be bounded Hermitean operators on Hilbert spaces Hi, 1≦i≦k, and let be the induced operators on . An important operator for multiparameter theory is δ: H →H denned by δ = det the determinant being expanded formally. Various definiteness properties of δ are critical for multiparameter spectral theory.We use the operators Aij to construct a numerical matrix δ(δ) upon which we use Geršgorin theory to investigate the non-singularity and definiteness of δ. Diagonal dominance properties of the array [Aij] are also discussed.
Publisher
Cambridge University Press (CUP)
Reference14 articles.
1. Another positivity result for determinantal operators
2. A GerSgorin inclusion set for the field of values of a finite matrix;Johnson;Proc. Amer. Math. Soc.,1973
3. 6 Farenick D. R. . Geršgorin Theory and Determinantal Operators (M.Sc. Thesis, University of Calgary, 1986).
4. A Recurring Theorem on Determinants
5. Multiparameter spectral theory in Hilbert space
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