Branch Mathematics and Statistics 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
Recommended Citation
Loring, Terry A. and Freddy Vides. "Estimating norms of commutators." (2013). https://digitalrepository.unm.edu/math_fsp/12
Comments
http://repository.unm.edu/handle/1928/23461
Article author is part of the Main Campus Math Department.