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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

An extension of the Weyl-von Neumann theorem to normal operators


Author: I. David Berg
Journal: Trans. Amer. Math. Soc. 160 (1971), 365-371
MSC: Primary 47.40
DOI: https://doi.org/10.1090/S0002-9947-1971-0283610-0
MathSciNet review: 0283610
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Abstract: We prove that a normal operator on a separable Hilbert space can be written as a diagonal operator plus a compact operator. If, in addition, the spectrum lies in a rectifiable curve we show that the compact operator can be made Hilbert-Schmidt.


References [Enhancements On Off] (What's this?)

  • [1] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933. MR 0270173 (42:5066)
  • [2] J. von Neumann, Charakterisierung des Spektrums eines Integraloperators, Actualités Sci. Indust., no. 229, Hermann, Paris, 1935.
  • [3] H. Weyl, Über beschränkte quadratischen Formen deren Differenz vollstetig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0283610-0
Keywords: Normal operator, diagonal operator, Hilbert-Schmidt, compact
Article copyright: © Copyright 1971 American Mathematical Society

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