On Two Equivalent Dilation Theorems in VH-Spaces
Complex Analysis and Operator Theory
625 - 650
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Please cite this item using this persistent URLhttp://hdl.handle.net/11693/21449
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.