Explore: Local Theory Of Banach Spaces

term "Banach space" and Banach in turn then coined the term "Fréchet space". Banach spaces originally grew out of the study of function spaces by Hilbert

of the interwar period (1918–1939). Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures

works on the local theory of Banach spaces, extending an idea going back to the work of Paul Lévy. It was further developed in the works of Milman and Gromov

probability theory by J. Hoffman–Jorgensen and in the characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier

especially as proved by Milman, is a milestone in the local (that is, finite-dimensional) theory of Banach spaces. While I feel sorry for a mathematician who cannot

In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional

generalizations of Banach spaces, which are complete vector spaces with respect to a metric generated by a norm. Metrizable topologies on vector spaces have been

(Riesz 1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Because of their key role in

areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed

theorems Complete space Cauchy sequence Banach fixed-point theorem Polish space Hausdorff distance Intrinsic metric Category of metric spaces Stone duality