Namespaces
Variants
Actions

Semi-bounded operator

From Encyclopedia of Mathematics
Revision as of 17:15, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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=16008
This article was adapted from an original article by V.I. Lomonosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article