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

• Autores: Morten Grud Rasmussen
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 111, Nº 1, 2012, págs. 107-117
• Idioma: inglés
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• Resumen

  • Let A be a ν-vector of self-adjoint, pairwise commuting operators and B a bounded operator of class Cn0(A). We prove a Taylor-like expansion of the commutator [B,f(A)] for a large class of functions f:Rν→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.