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- W1752843518 abstract "We consider contractions of complexified real cones, as recently introduced by Rugh in [Rugh10]. Dubois [Dub09] gave optimal conditions to determine if a matrix contracts a canonical complex cone. First we generalize his results to the case of complex operators on a Banach space and give precise conditions for the contraction and an improved estimate of the size of the associated spectral gap. We then prove a variational formula for the leading eigenvalue similar to the Collatz-Wielandt formula for a real cone contraction. Morally, both cases boil down to the study of suitable collections of 2 by 2 matrices and their contraction properties on the Riemann sphere." @default.
- W1752843518 created "2016-06-24" @default.
- W1752843518 creator A5085141473 @default.
- W1752843518 date "2010-11-23" @default.
- W1752843518 modified "2023-09-27" @default.
- W1752843518 title "Complexified Cones. Spectral gaps and variational principles." @default.
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