Estimating Norms of Commutators
arXiv:1301.4252
Abstract
We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y] assuming that x and y are contractions in a C*-algebra A, with x normal and with spectrum within the domain of f. In particular we discuss [x^2, y] and [x^(1/2), y] for 0 <=, x <=, 1. For larger values of δ= \|[x; y]\| we can rigorous calculate the best possible upper bound \|[f(x), y]\| for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the best upper bound.
We are posting the next version of this paper at : http://repository.unm.edu/handle/1928/23462. Also posted at http://repository.unm.edu is theMatlab code used to generate examples