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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A formally normal operator having no normal extension
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by Konrad Schmüdgen
Proc. Amer. Math. Soc. 95 (1985), 503-504
DOI: https://doi.org/10.1090/S0002-9939-1985-0806097-0
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Abstract:

We give an example of a formally normal operator $N$ satisfying $\dim \mathcal {D}({N^ * })/\mathcal {D}(N) = 1$ which has no normal extension in any larger Hilbert space.
References
  • Earl A. Coddington, Formally normal operators having no normal extensions, Canadian J. Math. 17 (1965), 1030–1040. MR 200719, DOI 10.4153/CJM-1965-098-8
    • K. Schmüdgen, Unbounded commutants and intertwining spaces of unbounded symmetric operators and $*$-representations (to appear). —, On commuting unbounded self-adjoint operators. III, Preprint, 1984; Manuscripta Math. (to appear).
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Bibliographic Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 95 (1985), 503-504
  • MSC: Primary 47B15; Secondary 47B37
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0806097-0
  • MathSciNet review: 806097