JournalszaaVol. 26, No. 4pp. 391–406

Multiplicative Perturbation by Contractions and Uniform Stability

  • P. C. M. Vieira

    National Laboratory for Scientific Computation, Petropolis, Brazil
  • C. S. Kubrusly

    Catholic University of Rio de Janeiro, Brazil
Multiplicative Perturbation by Contractions and Uniform Stability cover
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Abstract

Let TT be an arbitrary bounded linear transformation of a Hilbert space into itself. We investigate classes of contractions SS for which the spectral radius r(ST)r(ST) of the product STST is less than one. The main result gives a collection of necessary and sufficient conditions for r(ST)<1{r(ST)<1} when TT is multiplicatively perturbed by compact contractions SS. We also give either necessary or sufficient conditions for perturbation by other classes of Hilbert space contractions, such as those that include the symmetries (e.g., involutions, unitary operators, self-adjoint, normal and normaloid contractions) or the orthogonal projections (e.g., nonnegative contractions).

Cite this article

P. C. M. Vieira, C. S. Kubrusly, Multiplicative Perturbation by Contractions and Uniform Stability. Z. Anal. Anwend. 26 (2007), no. 4, pp. 391–406

DOI 10.4171/ZAA/1331