Eventually Cone-Positive Semigroups of Linear Operators.

We extend the theory of eventually nonnegative, eventually-exponentially nonnegative matrices and eventually positive semigroups to eventually cone-positive semigroups of linear operators on Banach lattices. We assume all the cones are proper and cone positivity is invariance of the cone under a given operator, while strong-cone-positivity is invariance of the interior of the cone. We examine the extension via properties of some classes of matrices, resolvent positive operators and Perron Frobenius type properties