Related papers: Self-Dual Cone Systems and Tensor Products

The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers.…

Based on the Archimedeanization developed by Paulsen and Tomforde, we give an explicit description for the positive cones of maximal tensor products of function systems. From this description, we obtain an approximation theorem for nuclear…

We discuss extensions of an inner product from a vector space to its full antidual. None of these extensions is weakly continuous, but partial extensions recapture some familiar structure including the Hilbert space completion and the…

We develop finite element spaces of symmetric tensor products of two-forms with polynomial coefficients. In three dimensions, these give higher order finite element spaces of matrix fields with normal-normal continuity, which have…

Let $F$ be an ordered topological vector space (over $\mathbb{R}$) whose positive cone $F_+$ is weakly closed, and let $E \subseteq F$ be a subspace. We prove that the set of positive continuous linear functionals on $E$ that can be…

We first show that every operation possesses an unique dual operation and measures an unique effect. If $a$ and $b$ are effects and $J$ is an operation that measures $a$, we define the sequential product of $a$ then $b$ relative to $J$.…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

In this paper, the tensor product of highest weight modules with intermediate series modules over the Neveu-Schwarz algebra is studied. The weight spaces of such tensor products are all infinitely dimensional if the highest weight module is…

In this paper, we describe the structural properties of the cone of $\mathcal{Z}$-transformations on the second order cone in terms of the semidefinite cone and copositive/completely positive cones induced by the second order cone and its…

We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently the class of operator systems that are associated with…

In this paper we study a class of convex sets which are called closed pseudo-cones and study a new duality of this class. It turns out that the duality characterizes closed pseudo-cones and is essentially the only possible abstract duality…

We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system. We begin with the…

Infinitary operations, such as products indexed by countably infinite linear orders, arise naturally in the context of fundamental groups and groupoids. Despite the fact that the usual binary operation of the fundamental group determines…

We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the…

We show the completeness of the system of generalized eigenfunctions of closed extensions of elliptic cone operators under suitable conditions on the symbols.

The state space of an operator system of $n$-by-$n$ matrices has, in a sense, many normal cones. Merely this convex geometrical property implies smoothness qualities and a clustering property of exposed faces. The latter holds since each…

Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…

In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two…

We prove that the 2-Deligne tensor product of two compact semisimple 2-categories exists. Further, under suitable hypotheses, we explain how to describe the $Hom$-categories, connected components, and simple objects of a 2-Deligne tensor…

The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…