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Necessary and sufficient conditions for spectral sets

  • Takayuki Furuta (a1) and Muneo Chō (a1)


We shall show necessary and sufficient conditions for which closed set X in the complex plane is a spectral set of an operator T on a complex Hilbert space.



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[1]Lebow, Arnold, “On von Neumann's theory of spectral sets”, J. Math. Anal. Appl. 7 (1963), 6490.
[2]von Neumann, Johann, “Eine Spektraltheorie für allegemeine Operatoren eines unitären Raumes”, Math. Nachr. 4 (1950/1951), 258281.
[3]Riesz, Frédéric et Sz.-Nagy, Béla, Legons d'analyse fonetionelle (Akadémiai Kiadó, Budapest, 1952).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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