Abstract. For an arbitrary strictly convex function f defined on the non-negative real line we determine the structure of all transformations on the set of density operators which preserve the quantum f -divergence.

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Abstract. We substantially extend and unify former results on the structure of surjective isometries of spaces of positive definite matrices obtained in the paper [14]. The isometries there correspond to certain geodesic distances in Finsler-type structures and to a recently defined interesting metric which also follows a nonEuclidean geometry. The novelty in our present paper is that here we consider not only true metrics but so-called generalized distance measures which are parameterized by unitarily invariant norms and continuous real functions satisfying certain conditions. Among the many possible applications, we shall see that using our new result it is easy to describe the surjective maps of the set of positive definite matrices that preserve the Stein's loss or several other types of divergences. We also present results concerning similar preserver transformations defined on the subset of all complex positive definite matrices with unit determinant.

Abstract. Motivated by recent investigations on norm-additive and spectrally multiplicative maps on various spaces of functions, in this paper we determine all bijective transformations between the positive cones of standard operator algebras over a Hilbert space which preserve a given symmetric norm of a given mean of elements. A result of similar spirit is also presented concerning transformations between cones of nonnegative elements of certain algebras of continuous functions.Mathematics Subject Classification (2010). Primary: 47B49. Secondary: 47A64, 26E60.

In recent years, ensemble weather forecasting has become a routine at all major weather prediction centers. These forecasts are obtained from multiple runs of numerical weather prediction models with different initial conditions or model parametrizations. However, ensemble forecasts can often be underdispersive and also biased, so some kind of postprocessing is needed to account for these deficiencies. One of the most popular state of the art statistical postprocessing techniques is the ensemble model output statistics (EMOS), which provides a full predictive distribution of the studied weather quantity. We propose a novel EMOS model for calibrating wind speed ensemble forecasts, where the predictive distribution is a generalized extreme value (GEV) distribution left truncated at zero (TGEV). The truncation corrects the disadvantage of the GEV distribution‐based EMOS models of occasionally predicting negative wind speed values, without affecting its favorable properties. The new model is tested on four datasets of wind speed ensemble forecasts provided by three different ensemble prediction systems, covering various geographical domains and time periods. The forecast skill of the TGEV EMOS model is compared with the predictive performance of the truncated normal, log‐normal and GEV methods and the raw and climatological forecasts as well. The results verify the advantageous properties of the novel TGEV EMOS approach.