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In https://www.encyclopediaofmath.org/index.php/Unitary_space, unitary space seems to be Hilbert space. But in http://www.answers.com/topic/unitary-space, "finite dimensional" is required. My question is, which definition of unitary space is commonly used?

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Answers.com is wrong. Unitary space is an archaic name for complex inner product space.

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    @PeteL.Clark sorry to drag this up, I'm trying to work out if my book has a typo for $(x,x)\ge 0$ - it has $(x,x)=0\iff x=0$, I guessed that "unitary space" was an archaic (old book) term for inner product but I am convinced that the requirement $(x|y)\ge 0$ is a typo, especially as $(x|y)=\overline{(y|x)}$ (what would $\ge$ mean her?) can you confirm? Also is the notation $(x|y)$ trivially translatable to $\langle x,y\rangle$? (It seems to be - I want a second opinion)2015-11-24