The role of domination and smoothing conditions in the theory of eventually positive semigroups

Daniel Daners, Jochen Glück
Preprint arXiv:1701.07309 [math.FA], January 2017
Bulletin of the Australian Mathematical Society 96 (2017), 286–298
Original article available at doi: 10.1017/S0004972717000260


We perform an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand we prove that, on many important function spaces, they imply compactness properties. On the other hand, we show that these conditions can be omitted in a number of Perron-Frobenius type spectral theorems. We furthermore prove a Kreĭn-Rutman type theorem on the existence of positive eigenvectors and eigenfunctionals under certain eventual positivity conditions.

AMS Subject Classification (2010): 47D06, 47B65, 34G10, 47A10

A preprint is available from arXiv:1701.07309 [math.FA].

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