Functional bases of numerical analysis : Hahn-Banach theorem

Hahn-Banach theorem
Functional bases of numerical analysis

Author : Claude BREZINSKI

Publication date: April 10, 2013 | Lire en français

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4. 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 T₁ and T₂ be two linear operators of domains D₁ and D₂ respectively. We'll say that T₂ is a linear extension of T₁ to D₂ if.

1. $D_{2} \supset D_{1}$ ,

2. ∀x ∊ D₁, T₂x = T₁x.

We also say that...

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Bibliography

(1) - BREZINSKI (C.) - Padé – Type Approximation and General Orthogonal Polynomials - ISNM, vol. 50, Birkhäuser-Verlag, Basel (1980).
(2) - BREZINSKI (C.) - Projection Methods for Systems of Equations - North-Holland, Amsterdam (1997).
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Hahn-Banach theorem Functional bases of numerical analysis

4. Hahn-Banach theorem

Bibliography

Hahn-Banach theorem
Functional bases of numerical analysis