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Proceedings of the American Mathematical Society

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



A formally normal operator having no normal extension

Author: Konrad Schmüdgen
Journal: Proc. Amer. Math. Soc. 95 (1985), 503-504
MSC: Primary 47B15; Secondary 47B37
MathSciNet review: 806097
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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 [Enhancements On Off] (What's this?)

  • Earl A. Coddington, Formally normal operators having no normal extensions, Canadian J. Math. 17 (1965), 1030–1040. MR 200719, DOI
  • 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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Keywords: Formally normal operator, unbounded normal operator
Article copyright: © Copyright 1985 American Mathematical Society