Semi-bounded operator
From Encyclopedia of Mathematics
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
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