IJPAM: Volume 56, No. 2 (2009)


Daniel J. Hay$^1$, Dan Kucerovsky$^2$
$^1$Department of Mathematics
State College
The Pennsylvania State University
109, McAllister Building, PA 16802, USA
e-mail: djh345@psu.edu
$^2$Department of Mathematics and Statistics
University of New Brunswick
Fredericton, NB, E3B 5A3, CANADA
e-mail: dkucerov@unb.ca

Abstract.Let $A$ and $B$ be operators in $\mathbf{B}(\mathfrak{H})$, with $A$ positive and invertible. We produce an estimate for the commutator $[A^\alpha,B]$ in terms of $\Vert[A,B]\Vert$ when $0 < \alpha < 1$. This estimate, when combined with a result for $\alpha \in \mathbb{N}$, establishes an estimate for any $\alpha \in \mathbb{R}^+$.

Received: August 23, 2009

AMS Subject Classification: 47A63, 46L05, 47L80

Key Words and Phrases: commutator estimates, operator theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 2