Positive finiteness-preserving surjective isometries on non-commutative symmetric spaces are projection disjointness preserving, enabling structural descriptions; similar results hold without positivity for strongly symmetric spaces with absolutely continuous norm.
Extension of projection mappings
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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 $I_2$ summands.
fields
math.OA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebras
Positive finiteness-preserving surjective isometries on non-commutative symmetric spaces are projection disjointness preserving, enabling structural descriptions; similar results hold without positivity for strongly symmetric spaces with absolutely continuous norm.