## Estimating norms of commutators

Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/23462

Title

Estimating norms of commutators

Author(s)

Loring, Terry A.

Vides, Freddy

Abstract

\begin{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.
\end{abstract}

Subject(s)

Commutators

matrix function

functional calculus

normal operator

spectral norm

Monte Carlo methods

matrix function

functional calculus

normal operator

spectral norm

Monte Carlo methods