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We extend the definitions of different types of quantum R\'enyi relative entropy from the finite dimensional setting of density matrices to density spaces of $C^*$-algebras. We show that those quantities (which trivially coincide in the classical commutative case) are essentially different on non-commutative algebras in the sense that none of them can be transformed to another one by any surjective transformation between density spaces. Besides, we determine the symmetry groups of density spaces corresponding to each of those quantum R\'enyi relative entropies and find that they are identical. Similar results concerning the Umegaki and the Belavkin-Staszewksi relative entropies are also presented., Comment: To appear in J. Funct. Anal

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms., Comment: To appear in J. Math. Anal. Appl

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum $\chi_\alpha^2$-divergence for some $\alpha \in [0,1]$. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

SUMMARY The authors investigated the helminth infection in 163 wild boars by analysing faecal samples with parasitological methods. The samples were collected in the 2009–2011 hunting season in the South-Mátra region of Hungary. Altogether 59 animals (36.19%) were found positive for Metastrongylus spp., 26 animals (15.95%) for Trichuris spp. and 22 animals (13.49%) for Oesophagostomum spp. Under one year of age 15 animals (40.54%) were found infected with Metasrtongylus spp., 11 animals (29.72%) with Trichuris spp. and 6 animals (16.21%) with Oesophagostomum spp. Metastrongylus-infection occurred more frequently among sows (31 animals: 52.54%), while Trichuris-infection (16 animals: 61.53%) and Oesophagostomum-infection (13 animals: 59.09%) was more prevalent among males

We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of surjective generalized isometries on $\mathbb{P}_2$ and, as second application, we complete another former result of ours on the structure of sequential endomorphisms of finite dimensional effect algebras.

In this article we consider certain kinds of metrics and relative entropies onsets of density operators acting on a finite-dimensional complex Hilbertspace. The metrics are the ones induced by the von Neumann?Schattenp-norms. We describe the general form of 'a priori' nonsurjective isometriesof the space of all density operators with respect to those distances. In thesecond part of this article we study mappings preserving entropicquantities. We determine the structure of 'a priori' nonsurjective maps onthe set of all density operators which leave a certain measure of relativeentropy invariant and also characterize the surjective maps on the set of allinvertible density operators with similar invariance properties