%0 Journal Article
%T Weak type estimates for the absolute value mapping
%A M. Caspers
%A D. Potapov
%A F. Sukochev
%A D. Zanin
%J Mathematics
%D 2013
%I arXiv
%X We prove that if A and B are bounded self-adjoint operators such that A-B belongs to the trace class, then |A| -|B| belongs to the principal ideal L_{1,\infty} in the algebra L(H) of all bounded operators on an infinite-dimensional Hilbert space generated by an operator whose sequence of eigenvalues is {1, 1/2, 1/3, 1/4, ...}. Moreover, \mu(j;|A| -|B|)\leq const(1 + j)^{-1}\|A-B\|_1. We also obtain a semifinite version of this result, as well as the corresponding commutator estimates.
%U http://arxiv.org/abs/1309.3378v2