# Aljoša Peperko: Generalizations of Krein-Rutman theorem

Date: 2. 1. 2017

Source: Algebra and functional analysis seminar

Source: Algebra and functional analysis seminar

Četrtek, 5. 1. 2017, ob 12:30 v predavalnici 2.03, FMF, Jadranska 21, Ljubljana

**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.

Vljudno vabljeni!

Roman Drnovšek in Primož Moravec