Spectral conditions for Jordan *-isomorphisms on operator algebras
In this paper we study non-linear transformations between the unitary groups of von Neumann algebras and the twisted subgroups of positive invertible elements in unital C∗-algebras with various preserver properties concerning the spectrum, spectral radius, and generalized distance measures. We present several results which show that those transformations are closely related to the Jordan *-isomorphisms between the underlying full algebras. In fact, our results can easily be used for characterizations of that sort of isomorphisms.