Every positive element of a von Neumann algebra that is integrable for an operator valued weight can be averaged by conjugating unitaries so that the weak closure of its orbit's convex hull meets the relative commutant, generalizing Marrakchi's theorem.
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Weak relative Dixmier property and Popa's intertwining technique for type III subfactors
Every positive element of a von Neumann algebra that is integrable for an operator valued weight can be averaged by conjugating unitaries so that the weak closure of its orbit's convex hull meets the relative commutant, generalizing Marrakchi's theorem.