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Similarity

In: An Introduction to Models and Decompositions in Operator Theory

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  • Carlos S. Kubrusly

    (Catholic University — PUC/RJ
    National Laboratory for Scientific Computation — LNCC)

Abstract

Which operators are similar to contractions? This is an important and difficult problem in operator theory (see [37, 38] and also [39, p.82]). In the present chapter we shall investigate two subproblems related to that one. For some classes of operators (e.g. compact or spectraloid) power boundedness is a necessary and sufficient condition for similarity to a contraction. However, by using the reducing subspace that was introduced in Foguel decomposition, we shall exhibit in Section 1 a power bounded operator that is not similar to any contraction. Such an operator will be used in turn to construct in Section 2 a strongly stable operator not similar to a contraction.

Suggested Citation

  • Carlos S. Kubrusly, 1997. "Similarity," Springer Books, in: An Introduction to Models and Decompositions in Operator Theory, chapter 0, pages 108-119, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1998-9_9
    DOI: 10.1007/978-1-4612-1998-9_9
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