nLab normal operator

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Definition

An element $a \in A$ in a C-star algebra is called normal if it commutes with its star-adjoint:

a \cdot a^* \;=\; a^* \cdot a \,.

The spectral theorem asserts, roughly, that (bounded) normal operators can be diagonalized.

Last revised on September 28, 2023 at 15:25:37. See the history of this page for a list of all contributions to it.