in 1908 schmidt published an important paper on infinitely many equations in infinitely many unknowns, introducing various geometric notations and terms which are still in use for describing spaces of functions and also in inner product spaces. schmidt's ideas were to lead to the geometry of hilbert spaces and he must certainly be considered as a founder of modern abstract functional analysis .

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In 1908 Schmidt published an important paper on infinitely many equations in infinitely many unknowns, introducing various geometric notations and terms which are still in use for describing spaces of functions and also in inner product spaces. Schmidt's ideas were to lead to the geometry of Hilbert spaces and he must certainly be considered as a founder of modern abstract functional analysis .