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2 results

  • JOINT SPECTRA OF REPRESENTATIONS OF LIE ALGEBRAS BY COMPACT OPERATORS

  • ENRICO BOASSO
  • Journal:
    Glasgow Mathematical Journal / Volume 46 / Issue 2 / May 2004
    Published online by Cambridge University Press:
    19 May 2004, pp. 355-362
    Print publication:
    May 2004
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  • Given $X$ a complex Banach space, $L$ a complex nilpotent finite dimensional Lie algebra, and $\rho\,{\colon}\, L\to L(X)$, a representation of $L$ in $X$ such that $\rho (l\,)\,{\in}\, K(X)$ for all $l\,{\in}\, L$, the Taylor, the Słodkowski, the Fredholm, the split and the Fredholm split joint spectra of the representation $\rho$ are computed.

  • An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators

  • Part of
  • Ali Ben Amor
  • Journal:
    Journal of the Australian Mathematical Society / Volume 75 / Issue 2 / October 2003
    Published online by Cambridge University Press:
    09 April 2009, pp. 233-246
    Print publication:
    October 2003
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  • Given two m-tuples of commuting spectral operators on a Hilbert space, T = (T1,…, Tm) and S = (S1,…, Sm), 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.