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I am reading basic sets. In the section of sesquilinear mapping, I came across this mapping $f: X \to X^*$ i.e $x \ $ maps to $ (x|.)$

Here I know $X$ is a function space, I guess $X^*$ stands for its dual. $(|)$ is inner mapping.

My question: What exactly is $(x|.)$?

Thanks in advance for the explanation.

Narasimham
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Prashanth
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  • It's the linear functional $(x |\cdot ): y\mapsto (x|y)$. At least, this is what I would say if $X$ was a vector space and $X^\ast$ is dual space. – Hayden Mar 08 '15 at 16:00

1 Answers1

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It is the map

$$\begin{array} .(x\:|\:\cdot): & X & \to & \mathbb{C} \\ & y & \mapsto & (x|y) \end{array}$$

Tryss
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