Aljoša Peperko: Generalizations of Krein-Rutman theorem

Abstract: We recall our main results, claiming that under suitable conditions the Bonsall cone spectral radius r(T) is included in the approximative point spectrum. As consequences, we obtain generalizations of Krein-Rutman theorem, claiming that, under suitable generalized compactness conditions, r(T) is a distinguished eigenvalue. In the proof we combine the methods of Mallet-Parret, Nussbaum (2003; maps on cones) and Feng (1997; nonlinear spectral theory on Banach spaces). If time allows, some open questions from  Mallet-Parret, Nussbaum (2010) will be outlined. The work presented is joint work with Vladimir M\"{u}ller.

 

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