Related papers: CP-Semigroups and Dilations, Subproduct Systems an…
The notion of a subproduct system, a generalization of that of a product system, is introduced. We show that there is an essentially 1 to 1 correspondence between cp-semigroups and pairs (X,T) where X is a subproduct system and T is an…
We study dilations of finite tuples of normal, completely positive and completely contractive maps (which we call CP-maps) acting on a von Neumann algebra, and commuting according to a graph G. We show that if G is acyclic, then a tuple…
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…
We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a…
Product systems have been originally introduced to classify E$_0$-semigroups on type I factors by Arveson. We develop the classification theory of E$_0$-semigroups on a general von Neumann algebra and the dilation theory of…
We study completely contractive representations of product systems of $C^*$-correspondences over semigroups. For a product system of $C^*$-correspondences over the semigroup $\mathbb{N}^2$, we prove that every such representation can be…
We prove that every strongly commuting pair of CP_0-semigroups has a minimal E_0-dilation. This is achieved in two major steps, interesting in themselves: 1: we show that a strongly commuting pair of CP_0-semigroups can be represented via a…
Consider $d$ commuting $C_{0}$-semigroups (or equivalently: $d$-parameter $C_{0}$-semigroups) over a Hilbert space for $d \in \mathbb{N}$. In the literature (\textit{cf.} [29, 26, 27, 23, 18, 25]), conditions are provided to classify the…
We introduce and study two-parameter subproduct and product systems of $C^*$-algebras as the operator-algebraic analogues of, and in relation to, Tsirelson's two-parameter product systems of Hilbert spaces. Using several inductive limit…
In this paper we propose a new technical tool for analyzing representations of Hilbert $C^*$-product systems. Using this tool, we give a new proof that every doubly commuting representation over $\mathbb{N}^k$ has a regular isometric…
This paper examines actions of right LCM semigroups by endomorphisms of C*-algebras that encode an additional structure of the right LCM semigroup. We define contractive covariant representations for these semigroup dynamical systems and…
Let E be a product system of C*-correspondences over N^r. Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between…
We give a necessary and sufficient criterion when a normal CP-map on a von Neumann algebra admits a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo's sufficient…
In a previous paper, we showed that every strongly commuting pair of CP_0-semigroups on a von Neumann algebra (acting on a separable Hilbert space) has an E_0-dilation. In this paper we show that if one restricts attention to the von…
Using ideas due to Jean-Luc Sauvageot, we prove the existence of a continuous unital dilation of a CP$_0$-semigroup on a separable W$^*$-algebra. This paper presents the material in the author's Ph. D. thesis (arXiv.org:1304.0134.pdf) with…
When S is a discrete subsemigroup of a discrete group G such that G = S^{-1} S, it is possible to extend circle-valued multipliers from S to G; to dilate (projective) isometric representations of S to (projective) unitary representations of…
We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We…
We report on a comparative study of the profile of the CKM unitarity triangle, and the resulting CP asymmetries in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), characterized by…
We introduce completely semi-$\varphi$-maps on Hilbert $C^*$-modules as a generalization of $\varphi$-maps. This class of maps provides examples of CP-extendable maps which are not CP-H-extendable, in Skeide-Sumesh's sense. Using the…
We prove that any weak* continuous semigroup $(T_t)_{t \geq 0}$ of factorizable Markov maps acting on a von Neumann algebra $M$ equipped with a normal faithful state can be dilated by a group of Markov $*$-automorphisms analogous to the…