Extension of projection mappings
Operator Algebras
2018-11-12 v1
Abstract
We show that a map between projection lattices of semi-finite von Neumann algebras can be extended to a Jordan -homomorphism between the von Neumann algebras if this map is defined in terms of the support projections of images (under the linear map) of projections and the images of orthogonal projections have orthogonal support projections. This has numerous fundamental applications in the study of isometries and composition operators on quantum symmetric spaces and is of independent interest, since it provides a partial generalization of Dye's Theorem without the requirement that the initial von Neumann algebra be free of type summands.
Cite
@article{arxiv.1811.04053,
title = {Extension of projection mappings},
author = {Pierre de Jager and Jurie Conradie},
journal= {arXiv preprint arXiv:1811.04053},
year = {2018}
}