Related papers: Unital q-positive maps on M_2(\C) and a related E_…
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)…
Powers has shown that each spatial E_0-semigroup can be obtained from the boundary weight map of a CP-flow acting on B(K \otimes L^2(0, \infty)) for some separable Hilbert space K. In this paper, we define boundary weight maps through…
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 E_0-semigroups which are not cocycle cocycle…
An E_0-semigroup is called q-pure if it is a CP-flow and its set of flow subordinates is totally ordered by subordination. The range rank of a positive boundary weight map is the dimension of the range of its dual map. Let K be a separable…
An $E_0$-semigroup of $B(H)$ is a one parameter strongly continuous semigroup of $*$-endomorphisms of $B(H)$ that preserve the identity. Every $E_0$-semigroup that possesses a strongly continuous intertwining semigroup of isometries is…
A partial description of the structure of positive unital maps $\phi: M_2(\bC) \to M_{n+1}(\bC)$ ($n\geq 2$) is given.
A map $\phi:M_m(\bC)\to M_n(\bC)$ is decomposable if it is of the form $\phi=\phi_1+\phi_2$ where $\phi_1$ is a CP map while $\phi_2$ is a co-CP map. It is known that if $m=n=2$ then every positive map is decomposable. Given an extremal…
Let $C=C(X)$ be the unital $C^*$-algebra of all continuous functions on a finite CW complex $X$ and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. We show that two unital monomorphisms $\phi, \psi: C\to A$ are…
Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We…
For two positive maps $\phi_i:B(\mathcal{K}_i)\to B(\mathcal{H}_i)$, $i=1,2$, we construct a new linear map $\phi:B(\mathcal{H})\to B(\mathcal{K})$, where $\mathcal{K}=\mathcal{K}_1\oplus\mathcal{K}_2\oplus\mathbb{C}$,…
Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…
Bhat characterizes the family of linear maps defined on $B(\mathcal{H})$ which preserve unitary conjugation. We generalize this idea and study the maps with a similar equivariance property on finite-dimensional matrix algebras. We show that…
A Q-system in a C* 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C* 2-categories called Q-system…
We analyze positivity of a tensor product of two linear qubit maps, $\Phi_1 \otimes \Phi_2$. Positivity of maps $\Phi_1$ and $\Phi_2$ is a necessary but not a sufficient condition for positivity of $\Phi_1 \otimes \Phi_2$. We find a…
Unital qubit Schwarz maps interpolate between positive and completely positive maps. It is shown that relaxation rates of qubit semigroups of unital maps enjoying Schwarz property satisfy the universal constraint which provides a…
Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple \CA with tracial rank zero. Suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We show that there is a continuous path of unitaries $\{u_t: t\in [0,…
Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
Let $A$ and $B$ be unital separable simple amenable \CA s which satisfy the Universal Coefficient Theorem. Suppose {that} $A$ and $B$ are $\mathcal Z$-stable and are of rationally tracial rank no more than one. We prove the following:…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…