Displaying similar documents to “On the structure of positive maps between matrix algebras”

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici

Similarity:

One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

Automatic continuity of biseparating maps

Jesús Araujo, Krzysztof Jarosz (2003)

Studia Mathematica

Similarity:

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

Multi-invertible maps and their applications

Mirosław Ślosarski (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.

Dissident maps on the seven-dimensional Euclidean space

Ernst Dieterich, Lars Lindberg (2003)

Colloquium Mathematicae

Similarity:

Our article contributes to the classification of dissident maps on ℝ ⁷, which in turn contributes to the classification of 8-dimensional real division algebras. We study two large classes of dissident maps on ℝ ⁷. The first class is formed by all composed dissident maps, obtained from a vector product on ℝ ⁷ by composition with a definite endomorphism. The second class is formed by all doubled dissident maps, obtained as the purely imaginary parts of the structures...

Finite-to-one maps and dimension

Jerzy Krzempek (2004)

Fundamenta Mathematicae

Similarity:

It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The...

Positive linear maps of matrix algebras

W. A. Majewski (2012)

Banach Center Publications

Similarity:

A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.

Decomposability of extremal positive unital maps on M₂(ℂ)

Władysław A. Majewski, Marcin Marciniak (2006)

Banach Center Publications

Similarity:

A map φ: Mₘ(ℂ) → Mₙ(ℂ) is decomposable if it is of the form φ = φ₁ + φ₂ where φ₁ is a CP map while φ₂ is a co-CP map. It is known that if m = n = 2 then every positive map is decomposable. Given an extremal unital positive map φ: M₂(ℂ) → M₂(ℂ) we construct concrete maps (not necessarily unital) φ₁ and φ₂ which give a decomposition of φ. We also show that in most cases this decomposition is unique.

Shadowing and expansivity in subspaces

Andrew D. Barwell, Chris Good, Piotr Oprocha (2012)

Fundamenta Mathematicae

Similarity:

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

Efficient generation of 3D surfel maps using RGB-D sensors

Artur Wilkowski, Tomasz Kornuta, Maciej Stefańczyk, Włodzimierz Kasprzak (2016)

International Journal of Applied Mathematics and Computer Science

Similarity:

The article focuses on the problem of building dense 3D occupancy maps using commercial RGB-D sensors and the SLAM approach. In particular, it addresses the problem of 3D map representations, which must be able both to store millions of points and to offer efficient update mechanisms. The proposed solution consists of two such key elements, visual odometry and surfel-based mapping, but it contains substantial improvements: storing the surfel maps in octree form and utilizing a frustum...