Zero product preservers of C*-algebras
Abstract
Description
Let T be be a zero-product preserving bounded linear map between C*-algebras A and B. Here neither A nor B is necessarily unital.
In this note, we investigate when T gives rise to a Jordan homomorphism. In particular, we show that A and B are isomorphic as Jordan algebras if T is bijective and sends zero products of self-adjoint elements to zero products. They are isomorphic as C*-algebras if T is bijective and preserves the full zero product structure.
4 pages,to appear in the ``Proceedings of the Fifth Conference on Function Space'', Contemporary Math
4 pages,to appear in the ``Proceedings of the Fifth Conference on Function Space'', Contemporary Math