Abstract
Let M be a von Neumann algebra and let (Lp(M),‖⋅‖p), 1≤p<∞ be Haagerup's Lp-space on M. We prove that the differentiability properties of ‖⋅‖p are precisely the same as those of classical (commutative) Lp-spaces. Our main instruments are multiple operator integrals and singular traces.
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