Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebras
Abstract
We show that positive surjective isometries between symmetric spaces associated with semi-finite von Neumann algebras are projection disjointness preserving if they are finiteness preserving. This is subsequently used to obtain a structural description of such isometries. Furthermore, it is shown that if the initial symmetric space is a strongly symmetric space with absolutely continuous norm, then a similar structural description can be obtained without requiring positivity of the isometry
URI
http://hdl.handle.net/10394/33555https://link.springer.com/article/10.1007/s11117-019-00711-2
https://doi.org/10.1007/s11117-019-00711-2