A taylor-like expansion of a commutator with a function of self-adjoint, pairwise commuting operators

Morten Grud Rasmussen


Let $A$ be a $\nu$-vector of self-adjoint, pairwise commuting operators and $B$ a bounded operator of class $C^{n_0}(A)$. We prove a Taylor-like expansion of the commutator $[B,f(A)]$ for a large class of functions $f\colon\mathbf{R}^\nu\to\mathbf{R}$, generalising the one-dimensional result where $A$ is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15216


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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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