Abstract
In this paper, we prove that every noncommutative L1-space associated to a finite von Neumann algebra can be renormed to satisfy the fixed point property for nonexpansive affine mappings. Particular examples are L1(R), where R is the hyperfinite II1 factor and the function spaces L1[0,1] and L1(μ) for any σ-finite measure space. This property does not hold for the usual ‖⋅‖1 norm.
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