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In 2008, J. Parcet showed the $(1,1)$ weak-boundedness of Calder\'on-Zygmundoperators acting on functions taking values in a von Neumann algebra. Wepropose a simplified version of his proof using the same tools : Cuculescu'sprojections and a pseudo-localisation theorem. This will unable us to recoverthe $L_p$-boundedness of Calder\'on-Zygmund operators with Hilbert valuedkernels acting on operator valued functions for $1 < p < \infty$ and an$L_p$-pseudo-localisation result of P. Hyt\"onen.

Weak boundedness of Calder\'on-Zygmund operators on noncommutative $L_1$-spaces