Topological vector spaces

normed vector space that is complete

vector space equipped with a compatible topology

theorem on extension of bounded linear functionals

theorem

locally convex space that is complete with respect to a translation-invariant metric

topological vector space in which every vector has a convex neighborhood

function space of all functions whose derivatives are rapidly decreasing

theorem

concept in calculus of variation

Hausdorff topological vector space for which every barrelled set in the space is a neighborhood for 0

In functional analysis, an F-space is a vector space X over the real or complex numbers together with a metric d : X \times X \to \R such that Scalar multiplication in X is continuous with respect to d and the standard metric on \R or \Complex. Addition in X is continuous with respect to d. The metric is translation-invariant; that is, d(x + a, y + a) = d(x, y) for all x, y, a \in X. The metric space (X, d) is complete.

generalization of the Lebesgue integral to Banach-space valued functions

Topologies on the set of operators on a Hilbert space

theorem that a continuous mapping of a convex subset of a topological vector space into a compact subset of itself has a fixed point

generalization of the concept of directional derivative, defined for functions between locally convex topological vector spaces

barrelled topological vector space where every closed and bounded set is compact

Hausdorff locally convex space such that tensor product with any other Hausdorff locally convex space is uniquely defined (i.e. the projective tensor product is canonically isomorphic to the injective tensor product)

weak topology on function spaces

dual pair of vector spaces

mathematical concept

space where bounded operators are continuous

space formed by the n-tuples of complex numbers

Generalization of the inverse function theorem