Tingley's problem for \(p\)-Schatten von Neumann classes (Q2662226)

Summary: Let \(H\) and \(H'\) be the complex Hilbert spaces. For \(p\in (1,\infty)\setminus \{2\}\), we consider the Banach space \(C_p(H)\) of all \(p\)-Schatten-von Neumann operators, whose unit sphere is denoted by \(S(C_p(H))\). We prove that every surjective isometry \(\Delta:S(C_p(H))\to S(C_p(H'))\) can be extended to a complex linear or to a conjugate linear surjective isometry \(T:C_p(H)\to C_p(H')\).