Any finite dimensional vector space V endowed with nondegenerate bilinear form can be canonically identified with its dual space.
I wonder if I can find similar identification for infinite dimensional vector spaces. For Hilbert spaces, the Riesz representation theorem gives an answer.
How about general infinite dimensional vector spaces endowed with nondegenerate (symmetric, if necessary) bilinear form?
In this case, the form does not induce a norm, and hence, a topology. Therefore I think what is critical here is to find suitable metric or topology so that one can deal with something like bounded(=continuous) linear functionals as in the Hilbert space case.