Faculty and Staff Publications

Document Type

Article

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 $0\leq x \leq 1$. 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.

Language (ISO)

English

Keywords

Commutators, matrix function, functional calculus, normal operator, spectral norm, Monte Carlo methods

Comments

http://repository.unm.edu/handle/1928/23461

Included in

Mathematics Commons

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