# A family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles

@article{Jankowski2010AFO, title={A family of non-cocycle conjugate E\_0-semigroups obtained from boundary weight doubles}, author={Christopher Jankowski}, journal={arXiv: Operator Algebras}, year={2010} }

We have seen that if \phi: M_n(\C) \rightarrow M_n(\C) is a unital q-positive map and \nu is a type II Powers weight, then the boundary weight double (\phi, \nu) induces a unique (up to conjugacy) type II_0 E_0-semigroup. Let \phi: M_n(\C) \rightarrow M_n(\C) and \psi: M_{n'}(\C) \rightarrow M_{n'}(\C) be unital rank one q-positive maps, so for some states \rho \in M_n(\C)^* and \rho' \in M_{n'}(\C)^*, we have \phi(A)=\rho(A)I_n and \psi(D) = \rho'(D)I_{n'} for all A \in M_n(\C) and D \in M_{n…

## One Citation

### Gauge groups of E_0-semigroups obtained from Powers weights

- Mathematics
- 2011

The gauge group is computed explicitly for a family of E_0-semigroups of type II_0 arising from the boundary weight double construction introduced earlier by Jankowski. This family contains many…

## References

SHOWING 1-10 OF 19 REFERENCES

### Unital q-positive maps on M_2(\C) and a related E_0-semigroup result

- Mathematics
- 2010

From previous work, we know how to obtain type II_0 E_0-semigroups using boundary weight doubles (\phi, \nu), where \phi: M_n(\C) \to M_n(\C) is a unital q-positive map and \nu is a normalized…

### Continuous spatial semigroups of completely positive maps of B(H)

- Mathematics
- 2003

This paper concerns the structure of strongly continuous one pa- rameter semigroups of completely positive contractions of B(H )= B(K ⊗ L2(0, ∞)) which are intertwined by translation. These are…

### CONSTRUCTION OF Eo-SEMIGROUPS OF B(H) FROM CP -FLOWS

- Mathematics

This paper constructs new examples of spatial Eo-semigroup of B(H) using CP -flows. A CP -flow is a strongly continuous one parameter semigroup of completely positive contractions of B(H) = B(K) ⊗…

### Generalized CCR Flows

- Mathematics
- 2008

We introduce a new construction of E0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C0-semigroups. We get a…

### Four Lectures on Noncommutative Dynamics

- Mathematics
- 2002

These lectures concern basic aspects of the theory of semigroups of endomorphisms of type $I$ factors that relate to causal dynamics, dilation theory, and the problem of classifying $E_0$-semigroups…

### The Index of a Quantum Dynamical Semigroup

- Mathematics
- 1997

A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index ofE0-semigroups. It is shown that the index of a unital completely positive semigroup…

### An Index Theory For Quantum Dynamical Semigroups

- Mathematics
- 1996

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…