Conjugations in space \(L^2\) of the unit circle commuting with multiplication by z or intertwining multiplications by z and \({{\bar{z}}}\) are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant for the unilateral shift and model spaces.

中文翻译：

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$$ L ^ 2 $$ L 2的共轭及其不变量

对单位圆的空间\（L ^ 2 \）中的共轭进行换乘，以z乘换或将z和\（{{{bar {z}}} \\）交织在一起。我们还研究了它们相对于Hardy空间，单边移位不变的子空间和模型空间的行为。