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Finite-Dimensional Extensions of Certain Symmetric Operators(1)

Published online by Cambridge University Press:  20 November 2018

I. M. Michael
I. M. Michael*
Affiliation:
The University, Dundee Scotland
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Let H be a Hilbert space with inner product 〈,). A well-known theorem of von Neumann states that, if S is a symmetric operator in H, then S has a selfadjoint extension in H if and only if S has equal deficiency indices. This result was extended by Naimark, who proved that, even if the deficiency indices of S are unequal, there always exists a Hilbert space H1 such that H ⊆ H1 and S has a selfadjoint extension in H1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 455 - 456
Copyright
Copyright © Canadian Mathematical Society 1973

Footnotes

(1)

Part of some research initiated while the author held a Post-doctoral Fellowship in McMaster University.

References

1. Coddington, E. A., Multi-valued operators and boundary value problems, Analytic theory of differential equations, Proceedings of the 1970 Conference at Western Michigan University, Kalamazoo, Lecture Notes in Mathematics 183, Springer-Verlag, Berlin, 1971.Google Scholar
2. Dunford, N. and Schwartz, J. T., Linear Operators, Part I, Interscience, New York, 1958.Google Scholar
3. Gilbert, R. C., Extremal spectral functions of a symmetric operator, Pacific J. Math. 14 (1964), 75–84.Google Scholar