VH-uzaylarında genleşme teoremleri

In the Appendix of the book Leçons d'analyse fonctionnelle by F. Riesz andB. Sz.-Nagy, B. Sz.-Nagy [15] proved an important theorem on operator valuedpositive definite maps on *-semigroups, which today can be considered as one ofthe pioneering results of dilation theory. In the same year W.F. Stinespring [11]proved another celebrated theorem about dilation of operator valued completelypositive linear maps on C*-algebras. Then F.H. Szafraniec [14] showed that thesetheorems are actually equivalent.Due to reasons coming from multivariate stochastic processes R.M. Loynes [7],considered a generalization of B. Sz.-Nagy's Theorem for vector Hilbert spaces(that he called VH-spaces). These VH-spaces have "inner products" that arevector valued, into the so-called "admissible spaces".This work is aimed at providing a detailed proof of R.M. Loynes Theorem thatgeneralizes B. Sz.-Nagy, a detailed proof of the equivalence of Stinespring's Theoremin the Arveson formulation [2] for B*-algebras with B. Sz.-Nagy's Theoremfollowing the lines in [14] together with some ideas from [2], and to get VH-variantsof Stinespring's Theorem for C*-algebras and B*-algebras. Relationsbetween these theorems are also considered.