Corollary 2

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

Topological Vector Spaces, chapter II, § 8. Complex locally convex spaces

— Let V be a vector subspace of a complex locally convex space E and f be a (complex) linear form defined and continuous in V; then there exists a continuous linear form $f_1$ defined in E and extending f. If E is normed there exists such a form $f_1$ that also satisfies $\|f_1\| = \|f\|$ .

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

Cited by

Nothing.

Cites

Nothing.