Hahn-Banach theorem

This is a rather straightforward consequence of the Hahn-Banach theorem.

We have the following consequence of the Hahn-Banach theorem.

As mentioned earlier, the axiom of choice implies the Hahn-Banach theorem.

By the Hahn-Banach theorem this set is nonempty.

Several properties of transposition depend upon the Hahn-Banach theorem.

The Hahn-Banach theorem shows that there exists a such that and .

This is a result of geometric nature and invokes the Hahn-Banach theorem (see reference below).

In mathematics, the Hahn-Banach theorem is a central tool in functional analysis.

This reveals the intimate connection between the Hahn-Banach theorem and convexity.

If is not dense in , then the Hahn-Banach theorem may sometimes be used to show that an extension exists.

The Hahn-Banach theorem, is one of fundamental theorems of functional analysis.

As a consequence of the Hahn-Banach theorem, this map is injective and isometric.

The Hahn-Banach theorem is equivalent to the following:

A famous example of a theorem of this sort is the Hahn-Banach theorem.

(to show this, the Hahn-Banach theorem is needed)

Local convexity is the minimum requirement for "geometrical" arguments like the Hahn-Banach theorem.

The mapping j is linear, and it is isometric by the Hahn-Banach theorem.

Hahn-Banach theorem .

The theorem has several important consequences, some of which are also sometimes called "Hahn-Banach theorem":

The main tool for proving the existence of continuous linear functionals is the Hahn-Banach theorem.

The Hahn-Banach theorem extends functionals from a subspace to the full space, in a norm-preserving fashion.

Together with the Hahn-Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field.

Alternate Version of Hahn-Banach theorem.

Moreover, the Hahn-Banach theorem implies the Banach-Tarski paradox.

In functional analysis the name Banach functional is used for sublinear function, especially when formulating Hahn-Banach theorem.