Let be a Hilbert space and let be a densely defined linear operator. Suppose that for some , there exists such that for all . Then such is unique, for if is another element of satisfying that condition, we have for all , which implies since is dense (http://planetmath.org/Dense). Hence we may define a new operator by
It is easy to see that is linear, and it is called the adjoint of .
Remark. The requirement for to be densely defined is essential, for otherwise we cannot guarantee to be well defined.
|Date of creation||2013-03-22 13:48:09|
|Last modified on||2013-03-22 13:48:09|
|Last modified by||Koro (127)|