Page "Alexander Grothendieck" Paragraph 28

Grothendieck's early mathematical work was in functional analysis.

Between 1949 and 1953 he worked on his doctoral thesis in this subject at Nancy, supervised by Jean Dieudonné and Laurent Schwartz.

His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of L < sup > p </ sup > spaces in studying linear maps between topological vector spaces.

In a few years, he had turned himself into a leading authority on this area of functional analysis — to the extent that Dieudonné compares his impact in this field to that of Banach.