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We have constructed a concrete example of a non-factorable positive operator. As a result, for the well-known problems (Ringrose, Kadison and Singer problems) we replace existence theorems by concrete examples.
There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected edge unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).
In [B1, Theorem 2.36] we proved the equivalence of six conditions on a continuous function f on an interval. These conditions define a subset of the set of operator convex functions, whose elements are called strongly operator convex. Two of the six
We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain posi
We prove a Fatou-type theorem and its converse for certain positive eigenfunctions of the Laplace-Beltrami operator $mathcal{L}$ on a Harmonic $NA$ group. We show that a positive eigenfunction $u$ of $mathcal{L}$ with eigenvalue $beta^2-rho^2$, $beta
Is it possible to form an image using light produced by stimulated emission? Here we study light scatter off an assembly of excited chromophores. Due to the Optical Theorem, stimulated emission is necessarily accompanied by excited state Rayleigh sca