Continuous functions of Hermitian operators

Halmos, P. R.

doi:10.1090/S0002-9939-1972-0288617-1

Continuous functions of Hermitian operators
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by P. R. Halmos

Proc. Amer. Math. Soc. 31 (1972), 130-132

DOI: https://doi.org/10.1090/S0002-9939-1972-0288617-1

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Abstract:

Theorem: every normal operator is a continuous function of a Hermitian one. Corollary: every normal operator on a separable Hilbert space is the sum of a diagonal operator and a compact one.

References

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Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
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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
K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
J. T. Schwartz, $W^{\ast }$-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 130-132
DOI: https://doi.org/10.1090/S0002-9939-1972-0288617-1
MathSciNet review: 0288617