Maximal and minimal extensions
From Encyclopedia of Mathematics
of a symmetric operator 
The operators 
(the closure of 
, cf. Closed operator) and 
(the adjoint of 
, cf. Adjoint operator), respectively. All closed symmetric extensions of 
occur between these. Equality of the maximal and minimal extensions is equivalent to the self-adjointness of 
(cf. Self-adjoint operator) and is a necessary and sufficient condition for the uniqueness of a self-adjoint extension.
Comments
References
| [a1] | M. Reed, B. Simon, "Methods of modern mathematical physics" , 1. Functional analysis , Acad. Press (1972) pp. Chapt. 8 |
How to Cite This Entry:
Maximal and minimal extensions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximal_and_minimal_extensions&oldid=32628
Maximal and minimal extensions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Maximal_and_minimal_extensions&oldid=32628
This article was adapted from an original article by A.I. LoginovV.S. Shul'man (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article