We show that the existence of a surjective isometry (which is merely a distance preserving
map) between the unitary groups of unital C∗-algebras implies the existence of a Jordan …

In this paper, we give an affirmative answer to Tingley's problem between finite von
Neumann algebras. To do this, we see that every norm closed proper face of the unit ball of …

arXiv:1303.7099v2 [math.GT] 22 Apr 2014 Page 1 Around groups in Hilbert Geometry
Ludovic Marquis Institut de Recherche Mathématique de Rennes email: ludovic.marquis@univ-rennes1.fr …

In this paper, we study geometric structures and isometries of the unit sphere of n× n
complex matrices. We introduce the notion of proper exposed points of the unit ball of a …

In this paper we study preserver transformations between positive definite cones in operator
algebras relating the spectral geometric mean of Fiedler and Pták. We also discuss kinds of …

Recently we have presented several structural results on certain isometries of spaces of
positive definite matrices and on those of unitary groups. The aim of this paper is to put those …

THE ARITHMETIC, GEOMETRIC AND HARMONIC MEANS IN OPERATOR ALGEBRAS
AND TRANSFORMATIONS AMONG THEM 1. Introduction The study of op Page 1 THE …

ISOMETRIES OF THE UNITARY GROUP 1. Introduction The classical Mazur-Ulam theorem
states that every surjective isometry T be- twe Page 1 PROCEEDINGS OF THE AMERICAN …

We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of
collineations (projectivities) if and only if the polyhedron is not an n-simplex with n≥ 2 …

Motivated by the famous Mazur-Ulam theorem in this paper we study algebraic properties of
isometries between metric groups. We present some general results on so-called $ d …