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I have a (infinite dimensional) vector space and defined an inner product on it.

The vectors element are infinite sequence of real numbers [tex](x_1, x_2,\ldots)[/tex].

The inner product has the common form: [tex]x_iy_i[/tex]

The problem now is that the vectors have an infinite number of elements, so the L2-norm of many vectors would be eventually equal to +Infinity.

- Is that admitted?

- How can one define anorthonormalbase for such a space?

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# L2 norm = +Infinity

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