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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
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.
- [1]
P.
R. Halmos, Ten problems in Hilbert
space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 0270173
(42 #5066), http://dx.doi.org/10.1090/S0002-9904-1970-12502-2
- [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.
- [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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DOI:
http://dx.doi.org/10.1090/S0002-9947-1971-0283610-0
PII:
S 0002-9947(1971)0283610-0
Keywords:
Normal operator,
diagonal operator,
Hilbert-Schmidt,
compact
Article copyright:
© Copyright 1971 American Mathematical Society
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