Explore: Modules De Banach

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace

open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental

finite-dimensional vector spaces. Every finite-dimensional subspace of a Banach space is complemented, but other subspaces may not. In general, classifying

III: The M-dimension can be 0 or ∞. Any two non-zero modules are isomorphic, and all non-zero modules are standard. Connes (1976) and others proved that

a paper that used Hilbert C*-modules to construct a theory of induced representations of C*-algebras. Hilbert C*-modules are crucial to Kasparov's formulation

every module has a basis. A module that has a basis is called a free module. Free modules play a fundamental role in module theory, as they may be used

nonnegative. Sublinear functions are often encountered in the context of the Hahn–Banach theorem. A real-valued function p : X → R {\displaystyle p:X\to \mathbb

generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces

one-forms. Modules are to rings what vector spaces are to fields: the same axioms, applied to a ring R instead of a field F, yield modules. The theory

of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear