Teorema Hahn-Banach untuk Fungsional Linier Terbatas

Rahmadita Widya Astuti, Dian Maharani, Abdul Aziz

Abstract


A linear functional  is a mapping from a vector space  to a field , ( or ), that satisfies two properties, additivity and homogeneity. Among the various properties of linear functionals, one important property is boundedness. This research is to prove the boundedness property of linear functionals using the Hahn-Banach Theorem. The Hahn-Banach Theorem addresses the extension of linear functionals. Thus, the results of this research show that with the Hahn-Banach Theorem, every element  in a normed space can be associated with a bounded linear functional  such that  dan . Furthermore, a linear functional defined on a real vector space can be extended to a complex vector space using the structure , and it is proven that this extension satisfies . This research is expected to be beneficial and serve as an additional reference.


Keywords


Hahn-Banach Theorem; Linear Functional; Bounded Linear Functional

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References


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DOI: https://doi.org/10.18860/jrmm.v5i3.34722

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