On two equivalent dilation theorems in VH-spaces
Ugurcan, B. E.
Complex Analysis and Operator Theory
625 - 650
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We 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.
Positive Semidefinite Complex
Complex Vector Space
Compact Hausdorff Space