Gheondea, A.Ugurcan, B. E.2016-02-082016-02-0820121661-8254http://hdl.handle.net/11693/21449We prove that a generalized version, essentially obtained by R. M. Loynes, of the B. Sz.-Nagy's Dilation Theorem for B*(H)-valued (here H is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W. F. Stinespring's Dilation Theorem for B*(H)-valued completely positive linear maps on B*-algebras. This equivalence result is a generalization of a theorem of F. H. Szafraniec, originally proved for the case of operator valued maps (that is, when H is a Hilbert space). © 2011 Springer Basel AG.EnglishOperator VersusPositive Semidefinite ComplexComplex Vector SpaceCompact Hausdorff SpaceBoundedness ConditionArticle10.1007/s11785-011-0191-91661-8262