Antiunitary operator

In mathematics, an antiunitary transformation, is a bijective antilinear map

between two complex Hilbert spaces such that

for all ${\displaystyle x}$ and ${\displaystyle y}$ in ${\displaystyle H_{1}}$, where the horizontal bar represents the complex conjugate. If additionally one has ${\displaystyle H_{1}=H_{2}}$ then U is called an antiunitary operator.

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