Rees Said The Formation Of The Theorem

The Riesz representation theorem is one of the important theorems in functional analysis. It’s pristine form conceived in1880, it was not until1909developed into a mature theorem. The formation of this theorem not only plays a positive promoting role in the development of the abstract analysis, but also makes significant changes in the object, content and methods of analytics. Nowadays the Riesz representation theorem, which main function is give the representation of the bounded linear functional on Hilbert space and establish an important connection between the Hilbert space and its continuous dual space. And its form from1909to the present has a metamorphosis. So it has an important meaning to research its period history from1880to1909.Based on the intensive investigation of original sources, present the basic work of Volterra, Phincherle and Bourlet on representation theorem, restore the represent theorem of Hadamard and Frechet. We can also found Riesz solved the problem which attacked by Hadamard and Frechet, and given the representation theorem in a real sense.