enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Hahn–Banach theorem - Wikipedia

    en.wikipedia.org/wiki/HahnBanach_theorem

    The theorem is named for the mathematicians Hans Hahn and Stefan Banach, who proved it independently in the late 1920s.The special case of the theorem for the space [,] of continuous functions on an interval was proved earlier (in 1912) by Eduard Helly, [1] and a more general extension theorem, the M. Riesz extension theorem, from which the HahnBanach theorem can be derived, was proved in ...

  3. Uniform boundedness principle - Wikipedia

    en.wikipedia.org/wiki/Uniform_boundedness_principle

    Together with the HahnBanach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators ) whose domain is a Banach space , pointwise boundedness is equivalent to uniform boundedness in operator norm .

  4. p-adic analysis - Wikipedia

    en.wikipedia.org/wiki/P-adic_analysis

    In many ways p-adic analysis is less subtle than classical analysis, since the ultrametric inequality means, for example, that convergence of infinite series of p-adic numbers is much simpler. Topological vector spaces over p-adic fields show distinctive features; for example aspects relating to convexity and the HahnBanach theorem are ...

  5. Functional analysis - Wikipedia

    en.wikipedia.org/wiki/Functional_analysis

    Together with the HahnBanach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space , pointwise boundedness is equivalent to uniform boundedness in operator norm.

  6. Continuous linear extension - Wikipedia

    en.wikipedia.org/wiki/Continuous_linear_extension

    Closed graph theorem (functional analysis) – Theorems connecting continuity to closure of graphs; Continuous linear operator; Densely defined operator – Function that is defined almost everywhere (mathematics) HahnBanach theoremTheorem on extension of bounded linear functionals

  7. Vector-valued Hahn–Banach theorems - Wikipedia

    en.wikipedia.org/wiki/Vector-valued_HahnBanach...

    In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued HahnBanach theorems are generalizations of the HahnBanach theorems from linear functionals (which are always valued in the real numbers or the complex numbers) to linear operators valued in topological vector spaces (TVSs).

  8. Open mapping theorem (functional analysis) - Wikipedia

    en.wikipedia.org/wiki/Open_mapping_theorem...

    In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem [1] (named after Stefan Banach and Juliusz Schauder), is a fundamental result that states that if a bounded or continuous linear operator between Banach spaces is surjective then it is an open map.

  9. Invariant subspace problem - Wikipedia

    en.wikipedia.org/wiki/Invariant_subspace_problem

    Many variants of the problem have been solved, by restricting the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces (in other words, each example, found so far, of an operator with no non-trivial invariant subspaces is an operator that acts on a ...