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We provide characterizations of convex, compact for the topology of local convergence in measure subsets of non-commutative L1-spaces previously considered for classical L1-spaces. More precisely, if M is a semifinite and σ-finite von Neumann algebra equipped with a distinguished semifinite faithful normal trace τ, P:M∗→L1(M,τ) is the non-commutative Yosida–Hewitt projection, and C is a norm bounded...
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