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Semi-bounded operator

From Encyclopedia of Mathematics
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A symmetric operator on a Hilbert space for which there exists a number such that

for all vectors in the domain of definition of . A semi-bounded operator always has a semi-bounded self-adjoint extension with the same lower bound (Friedrichs' theorem). In particular, and its extension have the same deficiency indices (cf. Defective value).

References

[1] F. Riesz, B. Szökefalvi-Nagy, "Functional analysis" , F. Ungar (1955) (Translated from French)
How to Cite This Entry:
Semi-bounded operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-bounded_operator&oldid=32353
This article was adapted from an original article by V.I. Lomonosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article