Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1985-0806097-0
MathSciNet review: 806097
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] Earl A. Coddington, Formally normal operators having no normal extensions, Canad. J. Math. 17 (1965), 1030–1040. MR 0200719, https://doi.org/10.4153/CJM-1965-098-8
  • [2] K. Schmüdgen, Unbounded commutants and intertwining spaces of unbounded symmetric operators and $ * $-representations (to appear).
  • [3] -, On commuting unbounded self-adjoint operators. III, Preprint, 1984; Manuscripta Math. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B15, 47B37

Retrieve articles in all journals with MSC: 47B15, 47B37


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0806097-0
Keywords: Formally normal operator, unbounded normal operator
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society