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On the extension of isometries between the unit spheres of von Neumann algebras

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We prove that every surjective isometry between the unit spheres of two von Neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras. Click to show full abstract

We prove that every surjective isometry between the unit spheres of two von Neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras.

Keywords: extension isometries; unit spheres; neumann algebras; von neumann

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018

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