Document Type

Dataset

Publication Date

12-2-2013

Abstract

We find estimates on the norm of a commutator of the form [f(x),y] in terms of the norm of [x,y], assuming that x and y are bounded linear operators on Hilbert space, with x normal and with spectrum within the domain of f. In particular we discuss |[x^2,y]| and |[x^{1/2},y]| for 0leq x leq 1. For larger values of delta = |[x,y]| we can rigorous calculate the best possible upper bound |[f(x),y]| leq eta_f(delta) 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.

Comments

Matlab code used to create test data in "Estimating norms of commutators."

Handle

http://hdl.handle.net/1928/23461

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