Tingley's problem for p-Schatten von Neumann classes

Abstract

[EN] Let H and H' be the complex Hilbert spaces. For p is an element of] 1, infinity[\{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)). In this paper we prove that every surjective isometry Delta: S(C-p(H)) -> S(C-p(H')) can be extended to a complex linear or to a conjugate linear surjective isometry T: C-p(H) -> C-p(H').