Related papers: A Continuity Theorem for Stinespring's Dilation

We prove lifting theorems for completely positive maps going out of exact $C^\ast$-algebras, where we remain in control of which ideals are mapped into which. A consequence is, that if $\mathsf X$ is a second countable topological space,…

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital…

On a W*-algebra M, for given two positive linear forms f,g and algebra elements a,b a variational expression for the Bures-distance d_B(f^a,g^b) between the inner derived positive linear forms f^a=f(a* . a) and g^b=g(b* . b) is obtained.…

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…

We derive a general obstruction to the existence of Riemannian metrics of positive scalar curvature on closed spin manifolds in terms of hypersurfaces of codimension two. The proof is based on coarse index theory for Dirac operators that…

We give a self-contained derivation of the Stinespring and Kraus structure theorems for completely positive maps using only scalar positive-definite kernels.

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2…

In the study of open quantum systems, one commonly describes the evolution of a system of interest through reduced dynamics, obtained by treating the environment indirectly rather than as a part of the full model. This thesis presents an…

We present an alternative (constructive) proof of the statement that for every completely positive, trace-preserving map $\Phi$ there exists an auxiliary Hilbert space $\mathcal K$ in a pure state $|\psi\rangle\langle\psi|$ as well as a…

We study the best approximation and distance problems in the operator space $\B(\HS)$ and in the space of trace class operators $\LS^1(\B(\HS))$. Formulations of distances are obtained in both cases. The case of finite-dimensional…

Let $C^*(\cls)$ be the $C^*$ algebra generated by an operator system $\cls$ i.e. a unital $*$-closed subspace of a unital $C^*$ algebra $\cla$. We prove that any complete order isomorphism $\cli:\cls \raro \cls'$ between two such operator…

Let \phi((x_1,x_2),(y_1,y_2))=(x_1-y_1)^2+(x_2-y_2)^2. We say that f:R^2 -> C^2 preserves distance d>=0 if for each x,y \in R^2 \phi(x,y)=d^2 implies \phi(f(x),f(y))=d^2. We prove that if x,y \in R^2 and |x-y|=(2\sqrt{2}/3)^k \cdot…

Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we…

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

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 study the structure of bipartite unitary operators which generate via the Stinespring dilation theorem, quantum operations preserving some given matrix algebra, independently of the ancilla state. We characterize completely the unitary…

In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is,…

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…

In this article, we introduce local completely positive $k$-linear maps between locally $C^{\ast}$-algebras and obtain Stinespring type representation by adopting the notion of "invariance" defined by J. Heo for $k$-linear maps between…

We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the relation. Here both "near" and "close" are in terms of the…