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Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras

Volume 235 / 2016

Peng Cao, Yurii V. Turovskii Studia Mathematica 235 (2016), 171-208 MSC: Primary 46H20, 46H15, 47A10; Secondary 4710, 22D25. DOI: 10.4064/sm8505-7-2016 Published online: 14 October 2016


A Jordan or associative algebra is called scattered if it consists of elements with countable spectrum (so called scattered elements). It is proved that for sub-Banach, Jordan or associative, algebras there exists the largest scattered ideal and it is closed. Accordingly, this determines the scattered topological radical. The characterization of the scattered radical is given, and the perturbation class of scattered elements is considered.


  • Peng CaoSchool of Mathematics and Statistics
    Beijing Institute of Technology
    Beijing, P.R. China
  • Yurii V. TurovskiiInstitute of Mathematics and Mechanics
    National Academy of Sciences of Azerbaijan
    9 Vahabzade Street
    Baku AZ1141, Azerbaijan

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