Relations between unitary $\rho$-dilatations and two norms

Correspondence between probabilistic norms and fuzzy norms

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

New relations between norms of system transfer functions

Relations between Renyi Distance and Fisher Information

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...

Relations between Sobolev and Kantorovich norms on manifolds with curvature conditions

We prove several multiplicative inequalities relating the Kantorovich norm with the Sobolev norm for functions on a Riemannian manifold satisfying certain curvature conditions.

Metric and classical fidelity uncertainty relations for random unitary matrices

We analyze uncertainty relations on finite dimensional Hilbert spaces expressed in terms of classical fidelity, which are stronger then metric uncertainty relations introduced by Fawzi, Hayden and Sen. We establish validity of fidelity uncertainty relations for random unitary matrices with optimal parameters (up to universal constants) which improves upon known results for the weaker notion of ...