Related papers: Extension of positive maps
Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
We define extension maps as maps that extend a system (through adding ancillary systems) without changing the state in the original system. We show, using extension maps, why a completely positive operation on an initially entangled system…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…
We employ the pinching theorem, ensuring that some operators A admit any sequence of contractions as an operator diagonal of A, to deduce/improve two recent theorems of Kennedy-Skoufranis and Loreaux-Weiss for conditional expectations onto…
In this paper, mirror extensions of vertex operator algebras is considered via tensor categories. The mirror extension conjecture is proved.
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…
We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover the case of some positive linear maps on a von Neumann algebra mapping any nonzero operator to an unbounded…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
In this paper we obtain several extension properties for monotone and sublinear operators. The results obtained generalize those known for positive and linear operators.
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with…
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie…
We present some foundations for a theory of real operator algebras and real Jordan operator algebras, and the various morphisms between these. A common theme is the ingredient of real positivity from papers of the first author with Read,…
We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…
We give conditions for when the tensor product of two positive maps between matrix algebras is a positive map. This happens when one map belongs to a symmetric mapping cone and the other to the dual cone. Necessary and sufficient conditions…
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…