Related papers: Separable states and positive maps II

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…

For an associative algebra $A$ with a simple module $M$ with trivial endomorphisms and trivial annihilator we verify the countable separation property (CSP), i.e. we prove that there exists a list of nonzero elements $a_1, a_2,\ldots$ of…

A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

Let H be a complex Hilbert space of dimension no less than 2 and B(H) be the algebra of all bounded linear operators on H. We give the form of surjective maps on B(H) preserving c-numerical range of operator products when the maps satisfy…

In previous articles, a magnetic pseudodifferential calculus and a family of C*-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol…

Let $E$ and $F$ be two Hilbert $C^*$-modules over $C^*$-algebras $A$ and $B$, respectively. Let $T$ be a surjective linear isometry from $E$ onto $F$ and $\varphi$ a map from $A$ into $B$. We will prove in this paper that if the…

We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.

Suppose that A is a C*-algebra for which A is isomorphic to A tensor Z, where Z is the Jiang-Su algebra: a unital, simple, stably finite, separable, nuclear, infinite dimensional C*-algebra with the same Elliott invariant as the complex…

A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

In the present paper we study the structure of C^*-algebras generated by the components of the polar decompositions of operators in Hilbert space satisfying certain commutation relations.

Let K be any compact set. The C^*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions…

We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\mathcal{K}_A(\mathsf{X})$…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their…

The full description of the set of positive maps $T: \qA \to \cB(\cH)$ ($\qA$ a $C^*$-algebra) is given. The approach is based on the simple prescription for selecting various types of positive maps. This prescription stems from the…