11 problems

Let $X$ be a Dedekind complete Banach lattice, and let $P\colon X\to X$ be a positive projection. Suppose there is an $b1\ge 0$ such that … and every positive operator $T$ satisfyi…

Bivariate Voronovskaja conjecture. One should have

Let $\mathbb{P}$ denote the cone of positive definite operators, let $\mathcal{P}^1(\mathbb{P})$ be the class of probability measures on $\mathbb{P}$ with finite first moment, let…

Let $T$ be an operator that is individually eventually positive, meaning that for every $x$ in the underlying ordered space there exists $N\in\mathbb{N}$ such that $T^n x$ is posit…

Let $H_n(\mathbb{R})^+$ denote the cone of real symmetric positive semidefinite $n\times n$ matrices. Let $\mathfrak{s}(C)$ be the cone of generators of one-parameter semigroups of…

Let $C$ be a symmetric cone, and let $B$ be an exotic drift, meaning an inward-pointing drift constructed in the paper that cannot be written as a sum of a Lie algebra element and…

Let $C\subseteq V$ be a symmetric cone. A linear map $B:V\to V$ is inward-pointing when … for all $u,v\in C$ satisfying $\langle u,v\rangle=0$. A Lie algebra element is a generator…

Conjecture B. The conclusions of Theorem 7.4 hold for this $m$; in particular, if $\varphi\in C(T_m)^+\setminus\{0\}$, then

Conjecture A. Theorem 7.1 holds for every $m\ge4$: the linear process ${\bf W}(t,\tau)$ on $X^{\wedge m}$ is $u_m$-positive with respect to $K_m$, and the corresponding quantity is…

For each $k\geq 0$, let $\mu_k^{(n)}$ be the dual functional associated with the monic eigenpolynomial $p_k^{(n)}$ of the Bernstein operator, and let $\mu_k^*$ be its limiting func…

Let $F_n$ be the positive linear operators under consideration, and let $C^3[0,1]$ denote the functions on $[0,1]$ with three continuous derivatives. Voronovskaya-type conjecture.…