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Proceedings of the American Mathematical Society

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

 
 

 

A semibounded closed symmetric operator whose square has trivial domain


Author: Paul R. Chernoff
Journal: Proc. Amer. Math. Soc. 89 (1983), 289-290
MSC: Primary 47B25
DOI: https://doi.org/10.1090/S0002-9939-1983-0712639-4
MathSciNet review: 712639
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Abstract: The existence of closed symmetric operators $ T$ such that $ D({T^2}) = (0)$ was shown by Naimark. This paper gives a simple, explicit construction for such operators and shows that $ T$ can be semibounded.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0712639-4
Article copyright: © Copyright 1983 American Mathematical Society

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