Related papers: Duality of cones of positive maps

In this paper the authors seek to trace in an accessible fashion the rapid recent development of the theory of the matrix geometric mean in the cone of positive definite matrices up through the closely related operator geometric mean in the…

We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the subject, we discuss how to model the compactly supported side…

Given a C$^*$-algebra $A$, let $S(A^+)$ denote the set of those positive elements in the unit sphere of $A$. Let $H_1$, $H_2,$ $H_3$ and $H_4$ be complex Hilbert spaces, where $H_3$ and $H_4$ are infinite-dimensional and separable. In this…

Let $\mathcal H$ be a complex Hilbert space and $\mathcal F_s (\mathcal H)$ the real vector space of all self-adjoint finite rank bounded operators on $\mathcal H$. We generalize the famous Wigner's theorem by characterizing linear maps on…

We determine the structure of all bijections on the cone of positive semidefinite operators which preserve the quantum $f$-divergence for an arbitrary strictly convex function $f$ defined on the positive halfline. It turns out that any such…

Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…

We reflect on the notions of positivity and square roots. We review many examples which underline our thesis that square roots of positive maps related to *-algebras are Hilbert modules. As a result of our considerations we discuss…

We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler…

We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of K\"ahler-Einstein metrics with cone singularities.

Let $X$ be a compact K\"{a}hler manifold, and let $L$ be a line bundle on $X.$ Define $I_k(L)$ to be the kernel of the multiplication map $ Sym^k H^0 (L) \to H^0 (L^k).$ For all $h \leq k,$ we define a map $\rho : I_k(L) \to Hom (H^{p,q}…

Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case in which…

Quadratic Hom-Lie algebras with equivariant twist maps are studied. They are completely characterized in terms of a maximal proper ideal that contains the kernel of the twist map and a complementary subspace to it that is either…

The class of stochastic maps, that is, linear, trace-preserving, positive maps between the self-adjoint trace class operators of complex separable Hilbert spaces plays an important role in the representation of reversible dynamics and…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the…

We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…

We establish spherical variants of the Gleason-Kahane-Zelazko and Kowalski-S{\l}odkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a…

In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…

This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of…

This paper aims to study the dual of an extended locally convex space. In particular, we study the weak and weak* topologies as well as the topology of uniform convergence on bounded subsets of an extended locally convex space. As an…

In this paper we study a generalization of K\"ahler differentials, which correspond to the secondary Hochschild homology associated to a triple $(A,B,\varepsilon)$. We establish computations in low dimension, while also showing how this…