• Corpus ID: 115165606

Product systems, subproduct systems and dilation theory of completely positive semigroups

@article{Shalit2010ProductSS,
  title={Product systems, subproduct systems and dilation theory of completely positive semigroups},
  author={Orr Moshe Shalit},
  journal={arXiv: Operator Algebras},
  year={2010}
}
  • O. Shalit
  • Published 26 February 2010
  • Mathematics
  • arXiv: Operator Algebras
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 second part deals with completely positive semigroups parameterized by quite general semigroups, where the major technical tool introduced is subproduct systems and their representations. In the third part subproduct systems are studied, together with the… 
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CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond

These notes are the output of a decade of research on how the results about dilations of one-parameter CP-semigroups with the help of product systems, can be put forward to d-parameter semigroups -…

References

SHOWING 1-10 OF 66 REFERENCES

QUANTUM MARKOV SEMIGROUPS: PRODUCT SYSTEMS AND SUBORDINATION

We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable…

ISOMETRIC DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS VIA COMMUTANTS

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…

On the product system of a completely positive semigroup

REGULAR DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS

  • B. Solel
  • Mathematics
    Mathematical Proceedings of the Royal Irish Academy
  • 2008
We study completely contractive representations of product systems $X$ of correspondences over the semigroup $\mathbb{Z}_+^k$. We present a necessary and sufficient condition for such a…

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

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 endomorphisms (E0-semigroups)…

E-dilation of strongly commuting CP-semigroups (the nonunital case)

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…

Continuous extension of a densely parameterized semigroup

AbstractLet $\mathcal{S}$ be a dense sub-semigroup of ℝ+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of…

One-parameter semigroups for linear evolution equations

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.-…

An Index Theory For Quantum Dynamical Semigroups

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 quantum dynamical semigroups…

Noncommutative Dynamics and E-Semigroups

Preface * Dynamical Origins * Part 1: Index and Perturbation Theory * E-semigroups * Continuous Tensor Products * Spectral C*-algebras * Part 2: Classification: Type I Cases * Path Spaces *…
...