Tingley's problem for spaces of trace class operators

Abstract

We prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces. This provides a positive solution to Tingley's problem in a new class of operator algebras.

References in corpus (4)

• Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces
• A solution to Tingley's problem for isometries between the unit spheres of compact C${}^{\ast }$-algebras and JB${}^{\ast }$-triples
• On the extension of isometries between the unit spheres of a C*-algebra and B(H)
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