Hahn-Banach theorem

Let X and Y be two vector spaces and T a linear operator from X into Y, with domain of definition $D_T\subset X$ . When inclusion is strict, the problem arises of extending T to a larger domain.

Definition 1

Let T ₁ and T ₂ be two linear operators of domains D ₁ and D ₂ respectively. We'll say that T ₂ is a linear extension of T ₁ to D ₂ if.

...