self-adjoint operator
A densely defined linear operator on a Hilbert space is a Hermitian or symmetric operator if for all . This means that the adjoint of is defined at least on and that its restriction to that set coincides with . This fact is often denoted by .
The operator is self-adjoint if it coincides with its adjoint, i.e. if . If is closable and its closure coincides with its adjoint (i.e. ), then is said to be essentially self-adjoint.
Title | self-adjoint operator |
Canonical name | SelfadjointOperator |
Date of creation | 2013-03-22 13:48:23 |
Last modified on | 2013-03-22 13:48:23 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 8 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 47B15 |
Classification | msc 47B25 |
Related topic | HermitianMatrix |
Defines | Hermitian operator |
Defines | symmetric operator |
Defines | essentially self-adjoint |
Defines | self-adjoint |