This condition is equivalent to stochastic mixability as well as the pseudoprobability convexity (PPC) condition, both defined by Van Erven et al. (2015). To be precise, for stochastic mixability, in Definition 4.1 of Van Erven et al. (2015), take their Fd and F both equal to our F , their P equal to {P}, and ψ(f) = f∗; then strong stochastic mixability holds. Likewise, for the PPC condition, i...

Given a Hamiltonian torus action the image of the momentum map is a convex polytope; this famous convexity theorem of Atiyah, Guillemin and Sternberg still holds when the action is not required to be Hamiltonian. Our generalization of the convexity theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and has as image a ...

If T is a bounded linear mapping (briefly, operator) in a Hilbert space 3C, the numerical range of T is the set WiT) = {(Tx, x): |[x|| = l}; thus WiT) is convex [8, p. 131], and its closure clfW^r)] is compact and convex. Roughly speaking, in this note we observe that cl[TF(T)] can be uniquely defined for an element T of an abstract C*-algebra, while WiT) cannot. The C*-algebra setting yields a...

Let G be a complex semisimple Lie group and τ a complex an-tilinear involution that commutes with the Cartan involution. If H denotes the connected subgroup of τ-fixed points in G, and K is maximally compact, each H-orbit in G/K can be equipped with a Poisson structure as described by Evens and Lu. We consider symplectic leaves of certain such H-orbits and show that an application of the symple...