A semibounded closed symmetric operator whose square has trivial domain
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- by Paul R. Chernoff PDF
- Proc. Amer. Math. Soc. 89 (1983), 289-290 Request permission
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.References
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- M. Neumark, On the square of a closed symmetric operator, C. R. (Doklady) Acad. Sci. URSS (N.S.) 26 (1940), 866–870. MR 0003468
- G. Szegö, Über die Randwerte einer analytischen Funktion, Math. Ann. 84 (1921), no. 3-4, 232–244 (German). MR 1512033, DOI 10.1007/BF01459407 K. Yosida, Functional analysis, 3rd ed., Springer-Verlag, Berlin and New York, 1971.
Additional Information
- © Copyright 1983 American Mathematical Society
- 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