Related papers: A completely positive map associated with a positi…

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

This paper is devoted to the generalization of the theory of total positivity. We say that a linear operator A in R^n is generalized totally positive (GTP), if its jth exterior power preserves a proper cone K_j in the corresponding space…

We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane…

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…

This work introduces and systematically studies a new convex cone of PCOP (pairwise copositive). We establish that this cone is dual to the cone of PCP (pairwise completely positive) and, critically, provides a complete characterization for…

A linear map $u\colon \ E\to F$ between operator spaces is called completely co-bounded if it is completely bounded as a map from $E$ to the opposite of $F$. We give several simple results about completely co-bounded Schur multipliers on…

A real matrix is said to be positive if its every entry is positive, and a real square matrix A is algebraically positive if there exists a real polynomial f such that f(A) is a positive matrix. A sign pattern matrix A is said to require a…

We classify all rational maps $H \in K(x)^n$ for which ${\rm trdeg}_K K(tH_1,tH_2,\ldots,tH_n) \le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such maps for which additionally $JH \cdot H = {\rm…

A graph is Schur-positive if its chromatic symmetric function expands non-negatively in the Schur basis. We determine a full Schur-positivity classification for complete multipartite graphs by showing that a complete multipartite graph…

We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $$u=\sum_{k=1}^\infty \langle u, y_k\rangle x_k,$$ then there exist nonzero scalars $\{\alpha_k\}_{k=1}^\infty$ such that…

We provide a characterization for operator valued completely bounded linear maps on Hilbert $C^*$-modules in terms of $\varphi$-maps. Also, we show that for every operator valued completely positive map $\varphi$ on a $C^*$-algebra…

A square matrix $A$ is completely positive if $A=BB^T$, where $B$ is a (not necessarily square) nonnegative matrix. In general, a completely positive matrix may have many, even infinitely many, such CP factorizations. But in some cases a…

A $k$-positive matrix is a matrix where all minors of order $k$ or less are positive. Computing all such minors to test for $k$-positivity is inefficient, as there are $\sum_{\ell=1}^k \binom{n}{\ell}^2$ of them in an $n\times n$ matrix.…

We will consider the set of all completely positive linear maps from a unital $C^*$-algebra to the $C^*$-algebra of all (bounded) adjointable right Hilbert $C^*$-module maps, which are automatically bounded, on a right Hilbert $C^*$-module…

This study investigates Hermitian linear maps, focusing on their decomposition into completely positive (CP) maps and their extensions to CP maps using auxiliary spaces. We derive a precise lower bound on the Hilbert-Schmidt norm of the…

We show that the pure state evaluation map from $ M_{n}(\mathbb{C}) $ to $ C(\mathbb{C} \mathbb{P}^{n-1}) $ (a completely positive map of $ C^{*} $-algebras) extends to a cochain map from the universal calculus on $ M_{n}(\mathbb{C} ) $ to…

We investigate certain classes of normal completely positive (CP) maps on the hyperfinite $II_1$ factor $\mathcal A$. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such…

Suppose a map $\phi$ on the set of positive definite matrices satisfies $\det(A+B)=\det(\phi(A)+\phi(B))$. Then we have $${\rm tr}(AB^{-1}) = {\rm tr}(\phi(A){\phi(B)}^{-1}).$$ Through this viewpoint, we show that $\phi$ is of the form…

We consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then…

This note defines a complete h-vector for convex polytopes, which extends the already known toric (or mpih) h-vector and has many similar properties. Complete means that it encodes the whole of the flag vector. First we define the concept…