Normal operator

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In functional analysis, a normal operator on a Hilbert space H (or more generally in a C* algebra) is a continuous linear operator that commutes with its hermitian adjoint N ^* :

The main importance of this concept is that the spectral theorem applies to normal operators.

Examples of normal operators:

• unitary operators ( N ^* = N ^{− 1} )
• Hermitian operators ( N ^* = N )
• positive operators (N = MM ^* )
• orthogonal projection operators (N = N ^* = N²)
• normal matrices can be seen as normal operators if one takes the Hilbert space to be Cⁿ.

[edit] See also

• Quasinormal operator
• Subnormal operator