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Fuglede’s theorem

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Abstract

In this short note, we give an elementary (set-theoretic) proof of Fuglede’s theorem that the commutant of a normal operator is *-closed.

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References

  1. B. Fuglede, A commutativity theorem for normal operators, Proc. of Nat. Acad. Sci., 36 (1950), 36–40.

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  2. P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York, (1974).

  3. C. R. Putnam, On normal operators in Hilbert space, Am. J. Math., 73 (1951), 35–36.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, Taramani, Chennai, 600 113, India

    V. S. Sunder

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  1. V. S. Sunder
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Correspondence to V. S. Sunder.

Additional information

Dedicated to Professor Kalyan B. Sinha on the occasion of his 70th birthday.

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Sunder, V.S. Fuglede’s theorem. Indian J Pure Appl Math 46, 415–417 (2015). https://doi.org/10.1007/s13226-015-0143-6

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  • DOI: https://doi.org/10.1007/s13226-015-0143-6

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