Spectral conditions for Jordan *-isomorphisms on operator algebras
Volume 236 / 2017
Studia Mathematica 236 (2017), 101-126
MSC: 47B49, 46L99.
DOI: 10.4064/sm8393-8-2016
Published online: 1 December 2016
Abstract
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 Jordan $^*$-isomorphisms between the underlying full algebras. In fact, our results can easily be used to characterize such isomorphisms.
