Dilation theory and continuous tensor product systems of Hilbert modules

M Skeide - Quantum Probability And Infinite-Dimensional Analysis, 2003 - World Scientific
The investigation of products systems of Hilbert modules as introduced by Bhat and Skeide6
has now reached a state where it seems appropriate to give a summary of what we know …

PRODUCT SYSTEMS: A SURVEY WITH COMMUTANTS IN VIEW

M Skeide - … Stochastics And Information: Statistics, Filtering and …, 2008 - World Scientific
The theory of product systems both of Hilbert spaces (Arveson systems) and product
systems of Hilbert modules has reached a status where it seems appropriate to rest a …

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

BVR Bhat, M Skeide - Infinite dimensional analysis, quantum …, 2000 - World Scientific
In this paper we study the problem of dilating unital completely positive (CP) semigroups
(quantum dynamical semigroups) to weak Markov flows and then to semigroups of …

Random sets and invariants for (type II) continuous tensor product systems of Hilbert spaces

V Liebscher - arXiv preprint math/0306365, 2003 - arxiv.org
In a series of papers Tsirelson constructed from measure types of random sets and
generalised random processes a new range of examples for continuous tensor product …

A simple proof of the fundamental theorem about Arveson systems

M Skeide - Infinite Dimensional Analysis, Quantum Probability and …, 2006 - World Scientific
With every E0-semigroup (acting on the algebra of of bounded operators on a separable
infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most …

[PDF][PDF] Dilations, products systems and weak dilations

MS Skeide - Math. Notes, 2002 - unimol.it
We generalize Bhat's construction of product systems of Hilbert spaces from E0–semigroups
on B (H) for some Hilbert space H to the construction of product systems of Hilbert modules …

Dilations, product systems, and weak dilations

M Skeide - Mathematical Notes, 2002 - Springer
We generalize Bhat's construction of product systems of Hilbert spaces from E 0-semigroups
on B (H) for some Hilbert space H to the construction of product systems of Hilbert modules …

The index of (white) noises and their product systems

M Skeide - Infinite Dimensional Analysis, Quantum Probability and …, 2006 - World Scientific
Almost every paper about Arveson systems (ie product systems of Hilbert spaces) starts by
recalling their basic classification assigning to every Arveson system a type and an index …

An index theory for quantum dynamical semigroups

B Bhat - Transactions of the American Mathematical Society, 1996 - ams.org
W. Arveson showed a way of associating continuous tensor product systems of Hilbert
spaces with endomorphism semigroups of type I factors. We do the same for general …

Commutants of von Neumann Modules, Representations of B^ a (E) and Other Topics Related to Product Systems of Hilbert Modules

M Skeide - arXiv preprint math/0308231, 2003 - arxiv.org
We review some of our results from the theory of product systems of Hilbert modules. We
explain that the product systems obtained from a CP-semigroup in a paper by Bhat and …