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In this paper, we determine the structure of certain algebraic morphisms and isometries of the spaceof allcomplex positive definite matrices. In the case, we describe all continuous Jordan triple endomorphisms ofwhich are continuous mapssatisfyingIt has recently been discovered that surjective isometries of certain substructures of groups equipped with metrics which are in a way compatible with the group operations have algebraic properties that relate them rather closely to Jordan triple morphisms. This makes us possible to use our structural results to describe all surjective isometries ofthat correspond to any member of a large class of metrics generalizing the geodesic distance in the natural Riemannian structure on. Finally, we determine the isometry group ofrelative to a very recently introduced metric that originates from the divergence called Stein’s loss. [ABSTRACT FROM AUTHOR]

In this article we consider the set of all positive semidefinite linear operators on a finite-dimensional complex Hilbert space equipped with the so-called logarithmic product. We describe the general form of all automorphisms of this structure which are continuous at 0. [ABSTRACT FROM AUTHOR]

In this article we consider certain kinds of metrics and relative entropies on sets of density operators acting on a finite-dimensional complex Hilbert space. The metrics are the ones induced by the von Neumann–Schatten p-norms. We describe the general form of ‘a priori’ nonsurjective isometries of the space of all density operators with respect to those distances. In the second part of this article we study mappings preserving entropic quantities. We determine the structure of ‘a priori’ nonsurjective maps on the set of all density operators which leave a certain measure of relative entropy invariant and also characterize the surjective maps on the set of all invertible density operators with similar invariance properties. [ABSTRACT FROM PUBLISHER]

We present a new simple proof of the structural result for elementary operators on standard operator algebras. Using the idea of this short proof we can characterize surjective maps between standard operator algebras having a certain multiplicativity-like property appearing in the abstract definition of elementary operators of length one. In particular, we show that such maps are automatically additive. [ABSTRACT FROM AUTHOR]