Hello, 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 an orthonormal base for such a space?