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

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

doi:10.4171/jst/313

JournalsjstVol. 10, No. 3pp. 809–841

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

Francisco J. Fernández-Polo
Universidad de Granada, Spain
Enrique Jordá
Universitat Politécnica de Valencia, Alcoy, Spain
Antonio M. Peralta
Universidad de Granada, Spain

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Abstract

Let $H$ and $H^{'}$ be the complex Hilbert spaces. For $p \in] 1, \infty [\ {2}$ 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 $Δ : S (C_{p} (H)) \to S (C_{p} (H^{'}))$ can be extended to a complex linear or to a conjugate linear surjective isometry $T : C_{p} (H) \to C_{p} (H^{'})$ .

Cite this article

Francisco J. Fernández-Polo, Enrique Jordá, Antonio M. Peralta, Tingley's problem for $p$ -Schatten von Neumann classes. J. Spectr. Theory 10 (2020), no. 3, pp. 809–841

DOI 10.4171/JST/313