J. Aust. Math. Soc.  75 (2003), 233-245
An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators

Ali Ben Amor
  Universität Bielefeld
  Fakultät für Mathematik
  33615 Bielefeld

Given two  m-tuples of commuting spectral operators on a Hilbert space, $T=(T_1,\ldots,T_m)$ and $S=(S_1,\ldots,S_m)$, an extended version of Henrici perturbation theorem is obtained for the joint approximate spectrum of $S$ under perturbation by $T$. We also derive an extended version of Bauer-Fike theorem for such tuples of operators. The method used involves Clifford algebra techniques introduced by McIntosh and Pryde.
Download the article in PDF format (size 101 Kb)

TeXAdel Scientific Publishing ©  Australian MS