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On the geometry of von Neumann algebra preduals
2013
Positivity (Dordrecht)
Let M be a von Neumann algebra and let M be its (unique) predual. We study when for every ϕ ∈ M there exists ψ ∈ M solving the equation ϕ ± ψ = ϕ = ψ . This is the case when M does not contain type I nor type III 1 factors as direct summands and it is false at least for the unique hyperfinite type III 1 factor. We also characterize this property in terms of the existence of centrally symmetric curves in the unit sphere of M of length 4. An approximate result valid for all diffuse von Neumann
doi:10.1007/s11117-013-0259-z
fatcat:zbfhswgarbh2jhxndj2dmwapxi