Representations of ∗-semigroups associated to invariant kernels with values adjointable operators
Linear Algebra and its Applications
361 - 388
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Please cite this item using this persistent URLhttp://hdl.handle.net/11693/25813
We 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.