Definition 2

Tag 07ZA, permanent. Cite it as [Bourbaki, Tag 07ZA].

Topological Vector Spaces, V, p. 18, § 2. Orthogonal families in a hilbertian space

A hilbertian space E is said to be a hilbertian sum of a family $(E_i)_{i \in I}$ of closed vector subspaces of E when :

1) for two distinct indices $i, k$ in I, the subspaces $E_i$ and $E_k$ are orthogonal in E; 2) the closed vector subspace generated by the union of the $E_i$ is E.

1 Care must be taken not to confuse this notation with that of the « algebraic » direct sum of the spaces $E_i$ (A, II, § 1, No. 6).

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

Cited by

Nothing.

Cites

II, § 1, No. 6