Tensor product systems of Hilbert modules and dilations of completely positive semigroups

By B. Bhat, Michael Skeide. 2000

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Dilation theory in finite dimensions: the possible, the impossible and the unknown (2010, methodology): “(K)PH ⊆ B(K). The following theorem is the the analogue of Sz.-Nagy’s Dilation Theorem appropriate for CP maps, and it is a key theorem in quantum dynamics. Theorem 6.2. Bhat’s Dilation Theorem1 (see [3, 4, 16, 22]). Every contractive CP map has a ∗-endomorphic dilation. The relation between Bhat’s ”
Inclusion systems and amalgamated products of product systems (2009, methodology): “Even while associating product systems to CP semigroups what one gets first are inclusion systems, and then an inductive limit procedure gives product system [8].”
Representations of product systems over semigroups and dilations of commuting CP maps (2005, unknown): “ar X iv :m at h/ 05 02 42 3v”
Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces (2003, background): “In the context of dilation theory, we should mention that the recent notion of tensor product systems of Hilbert modules of BHAT and SKEIDE [12] is deeply related to this topic too.”
Subproduct systems (2009, unknown): “In [14], Bhat and Skeide associate with every semigroup of completely positive maps on a C-algebra A a product system of Hilbert A-correspondences.”