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Let $H$ be a separable Hilbert space of square integrable functions from $T$ to $\mathbb{R}$. Is the following equality is true? $\left\langle f,g\right\rangle _{H}\left\langle f,g\right\rangle _{H}=\left\langle f,g\right\rangle _{H}^{2},f,g\in H$, or how we could simplify $\left\langle f,g\right\rangle _{H}\left\langle f,g\right\rangle _{H}$? Thank you in advance,

fina
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    Of course yo may write $\left\langle f,g\right\rangle _{H}\left\langle f,g\right\rangle _{H}=\left\langle f,g\right\rangle _{H}^{2}$. Or somewhat exotic $\left\langle f,g\right\rangle _{H}\left\langle f,g\right\rangle _{H}=\left\langle\left\langle f,g\right\rangle _{H} f,g\right\rangle _{H}$. – Michael Hoppe Nov 22 '20 at 15:45
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    $\langle f,g\rangle_H$ is a real number so of course $\left\langle f,g\right\rangle _{H}\left\langle f,g\right\rangle _{H}=\left\langle f,g\right\rangle _{H}^{2}$ is true. – mechanodroid Nov 22 '20 at 15:45
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    This is just the equality defining what the square is. – mathcounterexamples.net Nov 22 '20 at 15:46
  • Thank you so much to all, I know it is little thing – fina Nov 22 '20 at 16:08

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