An extension of the Weyl-von Neumann theorem to normal operators
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- by I. David Berg
- Trans. Amer. Math. Soc. 160 (1971), 365-371
- DOI: https://doi.org/10.1090/S0002-9947-1971-0283610-0
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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
- P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 270173, DOI 10.1090/S0002-9904-1970-12502-2 J. von Neumann, Charakterisierung des Spektrums eines Integraloperators, Actualités Sci. Indust., no. 229, Hermann, Paris, 1935. H. Weyl, Über beschränkte quadratischen Formen deren Differenz vollstetig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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