ABSTRACT
We now prove the Hahn - Banach Theorem and several of its corollaries. The Hahn - Banach Theorem is a fundamental result in analysis. A typical but important application of the Hahn - Banach Theorem is its use in the proof that linear functionals on certain linear spaces can be represented in the useful “inner product” form, or as a pairing between the space and its dual space. There are many special cases of the Hahn - Banach Theorem, some of which we will prove as corollaries.
