Cohomology of nilpotent subalgebras of affine lie algebras

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Abstract

Let T be an operator on a Hubert space. We show that the pair (T, T) can be perturbed to an invertible pair if and only if T is Fredholm of index zero. We also exhibit a large class of Fredholm n-tuples acting on a Banach space which cannot be perturbed by finite rank operators to invertible ones.

Original languageEnglish
Pages (from-to)195-198
Number of pages4
JournalProceedings of the American Mathematical Society
Volume122
Issue number1
DOIs
StatePublished - Sep 1994

Keywords

  • Compact perturbation
  • Fredholm n-tuple
  • Index zero

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