Related papers: Mapping Cones are Operator Systems
The well-known theory of "rational canonical form of an operator" describes the invariant factors, or elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space $\V$ over a…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…
We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian systems. For finite dimensional operators, a novel concept of…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
In this article we consider means of positive operators on a Hilbert space. We extend the theory of matrix power means to arbitrary operator means in the sense of Kubo-Ando. The basis of the extension is relying on ideas coming from…
Probability maps are additive and normalised maps taking values in the unit interval of a lattice ordered Abelian group. They appear in theory of affine representations and they are also a semantic counterpart of Hajek's probability logic.…
We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other.…
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…
We characterize a set of positive maps in matrix algebra of 4x4 complex matrices. Equivalently, we provide a subset of entanglement witnesses parameterized by the rotation group SO(3). Interestingly, these maps/witnesses define two…
We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices which maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality…
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 systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
Two notions for linear maps (operational convex combinations and operational exetreme points) are introduced. The set S of ucp maps on the n times n matrix algebra is the operational convex combinations of the identity map. An operational…
Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive…