Weak boundedness of Calderón-Zygmund operators on noncommutative L1-spaces

In 2008, J. Parcet showed the (1,1) weak-boundedness of Calderón-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools: Cuculescu's projections and a pseudo-localisation theorem. This will unable us to recover the Lp-boundedness of Calderón-Zygmund operators with Hilbert valued kernels acting on operator valued functions for 1