Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebras

Pierre de Jager; Jurie Conradie

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arXiv · 1907.06452

Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebras

Pierre de Jager·Jurie Conradie

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Abstract

In this article 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.

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BibTeX RIS

Pierre de Jager, Jurie Conradie. 2019-07-15. Isometries between non-commutative symmetric spaces associated with semi-finite von Neumann algebras. https://arxiv.org/abs/1907.06452

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