Ay, S.Gheondea, A.2016-02-082016-02-0820150024-3795http://hdl.handle.net/11693/25813We consider positive semidefinite kernels valued in the ∗-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of ∗-semigroups. A rather general dilation theorem is stated and proved: for these kind of kernels, representations of the ∗-semigroup on either the VE-spaces of linearisation of the kernels or on their reproducing kernel VE-spaces are obtainable. We point out the reproducing kernel fabric of dilation theory and we show that the general theorem unifies many dilation results at the non-topological level. © 2015 Elsevier Inc.Englishprimary 47A20secondary 15B48Ordered ∗-spaceVE-spacePositive semidefinite kernel∗-semigroupInvariant kernelLinearisation∗-representation43A35Reproducing kernelOrdered ∗-algebraVE-moduleArticle10.1016/j.laa.2015.08.0121873-1856