Tingley's problem through the facial structure of operator algebras
By Michiya Mori. Journal of Mathematical Analysis and Applications, 2017
49 citations recorded by the source corpus.
Abstract Tingley's problem asks whether every surjective isometry between the unit spheres of two Banach spaces admits an extension to a real linear surjective isometry between the whole spaces. In this paper, we give an affirmative answer to Tingley's problem when both spaces are preduals of von Neumann algebras, the spaces of self-adjoint operators in von Neumann algebras or the spaces of self-adjoint normal functionals on von Neumann algebras. We also show that every surjective isometry between the unit spheres of unital C⁎-algebras restricts to a bijection between their unitary groups. In addition, we show that every surjective isometry between the normal state spaces or the normal quasi-state spaces of two von Neumann algebras extends to a linear surjective isometry.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/02998cf0a6fa8fa36bb16e866473590cb2149fc6
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- A survey on Tingley’s problem for operator algebras (2018, background): “Mori (see [33]), which has been an impressive discovering, and made this autor change the original project to insert some nice achievements, one of them is a positive solution to Tingley’s problem for preduals of general von Neumann algebras (see Theorem 4.”