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Perturbation Theory for Quasinilpotents in Banach Algebras

Author

Listed:
  • Xin Wang

    (School of Artificial Intelligence, Jianghan University, Wuhan 430056, China)

  • Peng Cao

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China
    Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 102488, China)

Abstract

In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then q n = 0 . Applications to C* algebras are given.

Suggested Citation

  • Xin Wang & Peng Cao, 2020. "Perturbation Theory for Quasinilpotents in Banach Algebras," Mathematics, MDPI, vol. 8(7), pages 1-7, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1163-:d:384925
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    References listed on IDEAS

    as
    1. Sin-Ei Takahasi, 1984. "Finite dimensionality in scole of Banach algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-4, January.
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