Consider a Hilbert space $H=L^2(\mathbb{R}_+)$, take its conjugate $\overline{H} := \left\{f^{+}, f \in H \right\}$, where $+$ stands for the conjugation. Space $\overline{H}$ is a Hilbert space with an inner product $\left
Complex conjugate of the Hilbert space
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functional-analysis
hilbert-spaces
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0What does $f^{+}$ mean? – 2012-11-30
1 Answers
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If $H$ is a Hilbert space then $H \otimes \bar{H}$ can be identified with Hilbert Schmidt operators on $H$ (sometimes denoted by $B_2(H)$), $\left| A \right> \left< B \right| \in B_2(H)$ corresponds to $A \otimes B^+ \in H \otimes \bar{H}$. I hope it answers most of your questions.