Related papers: Tensor Products of Convex Cones
We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where $\mathscr H^n$ is a Hadamard manifold.…
An original presentation of Categorical Quantum Physics, in the line of Abramsky and Coecke, tries to introduce only objects and assumptions that are clearly relevant to Physics and does not assume compact closure. Adjoint arrows, tensor…
A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
Matrix convexity generalizes convexity to the dimension free setting and has connections to many mathematical and applied pursuits including operator theory, quantum information, noncommutative optimization, and linear control systems. In…
For valuations on convex bodies in Euclidean spaces, there is by now a long series of characterization and classification theorems. The classical template is Hadwiger's theorem, saying that every rigid motion invariant, continuous,…
We analyse the convex structure of the Finsler infinitesimal balls of the Thurston metric on Teichm{\"u}ller space. We obtain a characterisation of faces, exposed faces and extreme points of the unit spheres. In particular, we prove that…
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
In this note, we show that the strong Viterbo conjecture holds true on any convex toric domain, and that the Viterbo's volume-capacity conjecture holds for the product of a $1$-unconditional convex body $A\subset\mathbb{R}^{n}$ and its…
In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and based on the notion of signatures of hermitian forms [1]. In…
In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…
We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference…
We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.
The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…
We classify the orbits of elements of the tensor product spaces ${\mathbb{F}}^2\otimes {\mathbb{F}}^3 \otimes {\mathbb{F}}^3$ for all finite; real; and algebraically closed fields under the action of two natural groups. The result can also…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…