  In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund
operators acting over operator-valued functions. Our main tools for its
solution are a noncommutative form of Calderon-Zygmund decomposition in
conjunction with a pseudo-localization principle for singular integrals, which
is new even in the classical setting and of independent interest. Perhaps
because of the hidden role of pseudo-localization and almost orthogonality,
this problem has remained open for quite some time. We also consider
Calderon-Zygmund operators associated to certain operator-valued kernels.
