Example

Tag 080O, permanent. Cite it as [Bourbaki, Tag 080O].

Topological Vector Spaces, V, p. 32, § 3. Tensor product of hilbertian spaces

— With the notations of example 1 of V, p. 32, we can identify the hilbertian space $\hat{\Lambda}(E)$ with the set of all sequences $(f_n)_{n \geq 0}$ of measurable functions for which the number $\|f\|$ defined in (22) is finite, and where each function $f_n$ is antisymmetric, that is, satisfies the relation

f_n(x_{\sigma(1)}, ..., x_{\sigma(n)}) = \varepsilon_\sigma f_n(x_1, ..., x_n)

for every permutation $\sigma \in \mathfrak{S}_n$ . The hilbertian space $\hat{\Lambda}(E)$ is called the antisymmetric Fock space corresponding to the weight $\omega$ . \*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

V, p. 32