Zero product preservers of C*-algebras
Operator Algebras
2007-08-29 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.0708.3718,
title = {Zero product preservers of C*-algebras},
author = {Ngai-Ching Wong},
journal= {arXiv preprint arXiv:0708.3718},
year = {2007}
}
Comments
4 pages,to appear in the ``Proceedings of the Fifth Conference on Function Space'', Contemporary Math