Tingley's problem for $p$-Schatten von Neumann classes

Francisco J. Fernández-Polo; Enrique Jordá; Antonio M. Peralta

Tingley's problem for $p$-Schatten von Neumann classes

Functional Analysis 2018-05-04 v2 Operator Algebras

Authors: Francisco J. Fernández-Polo , Enrique Jordá , Antonio M. Peralta

Abstract

Let $H$ and $H'$ be a complex Hilbert spaces. For $p\in(1, \infty)\backslash\{2\}$ 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 $T:C_p(H)\to C_p(H')$ .

Keywords

lp spaces and inequalities banach spaces

Cite

@article{arxiv.1803.00763,
  title  = {Tingley's problem for $p$-Schatten von Neumann classes},
  author = {Francisco J. Fernández-Polo and Enrique Jordá and Antonio M. Peralta},
  journal= {arXiv preprint arXiv:1803.00763},
  year   = {2018}
}

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