of a symmetric operator $A$

The operators $\bar A$ (the closure of $A$, cf. Closed operator) and $A^*$ (the adjoint of $A$, cf. Adjoint operator), respectively. All closed symmetric extensions of $A$ occur between these. Equality of the maximal and minimal extensions is equivalent to the self-adjointness of $A$ (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
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