Positivity https://doi.org/10.1007/s11117-017-0547-0 Positivity C 0 -semigroups associated with uniquely ergodic Kantorovich modifications of operators Margareta Heilmann 1 · Ioan Ra¸ sa 2 Received: 25 June 2017 / Accepted: 28 November 2017 © Springer International Publishing AG, part of Springer Nature 2017 Abstract We extend to the context of L p spaces and C 0 -semigroups of operators our previous results from Heilmann and Ra¸ sa (Positivity 21:897–910, 2017. https:// doi.org/10.1007/s11117-016-0441-1), concerning the eigenstructure and iterates of uniquely ergodic Kantorovich modifications of linking operators. Keywords Linking operators · Kantorovich modification · Uniquely ergodic operator · Iterates of operators · C 0 -semigroups Mathematics Subject Classification 37A30 · 41A36 1 Introduction In a previous paper [7] we considered a family of operators which constitute a non- trivial link between the genuine Bernstein–Durrmeyer operators and the classical Bernstein operators. We proved that the Kantorovich type modifications of these linking operators are uniquely ergodic and investigated their eigenstructure. As a consequence, it was possible to determine the limit of the iterates of such a modified operator and to relate it to the corresponding unique invariant measure. We provided B Margareta Heilmann heilmann@math.uni-wuppertal.de Ioan Ra¸ sa ioan.rasa@math.utcluj.ro 1 School of Mathematics and Natural Sciences, University of Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany 2 Department of Mathematics, Technical University, Str. Memorandumului 28, 400114 Cluj-Napoca, Romania