ABSTRACT
Let be a JBW-algebra. For
, let
denote the quadratic operator defined by
. We show that if
has no abelian direct summand, then every bijection φ from the positive cone of
onto the positive cone of a JBW-algebra
satisfying
for all positive elements
extends to a Jordan isomorphism from
onto
.
Acknowledgments
The authors express their sincere thanks to the reviewers for their careful reading and their valuable comments and suggestions towards to the improvement of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.