TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT

Talakua, Mozart W.
Nanuru, Stenly J.

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 5 No 2 (2011): BAREKENG : Jurnal Ilmu Matematika dan Terapan

Hilbert space is a very important idea of the Davids Hilbert invention. In 1907, Riesz and Fréchet developed one of the theorem in Hilbert space called the Riesz-Fréchet representationtheorem. This research contains some supporting definitions Banach space, pre-Hilbert spaces, Hilbert spaces, the duality of Banach and Riesz-Fréchet representation theorem. On Riesz-Fréchet representation theorem will be shown that a continuous linear functional that exist in the Hilbert space is an inner product, in other words, there is no continuous linear functional on a Hilbert space except the inner product.