closed graph theorem


closed graph theorem
Математика: теорема о замкнутом графике (в функциональном анализе)

Универсальный англо-русский словарь. . 2011.

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  • Closed graph theorem — In mathematics, the closed graph theorem is a basic result in functional analysis which characterizes continuous linear operators between Banach spaces in terms of the operator graph. Contents 1 The closed graph theorem 2 Generalization 3 See… …   Wikipedia

  • Closed operator — In mathematics, specifically in functional analysis, closed linear operators are an important class of linear operators on Banach spaces. They are more general than bounded operators, and therefore not necessarily continuous, but they still… …   Wikipedia

  • Graph of a function — In mathematics, the graph of a function f is the collection of all ordered pairs ( x , f ( x )). In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane,… …   Wikipedia

  • Graph coloring — A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called colors to elements of a graph… …   Wikipedia

  • graph theory — Math. the branch of mathematics dealing with linear graphs. [1965 70] * * * Mathematical theory of networks. A graph consists of nodes (also called points or vertices) and edges (lines) connecting certain pairs of nodes. An edge that connects a… …   Universalium

  • Open mapping theorem (functional analysis) — In functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem (named after Stefan Banach and Juliusz Schauder), is a fundamental result which states that if a continuous linear operator between Banach spaces is… …   Wikipedia

  • Hellinger–Toeplitz theorem — In functional analysis, a branch of mathematics, the Hellinger–Toeplitz theorem states that an everywhere defined symmetric operator on a Hilbert space is bounded. By definition, an operator A is symmetric if : langle A x | y angle = langle x | A …   Wikipedia

  • Bounded inverse theorem — In mathematics, the bounded inverse theorem is a result in the theory of bounded linear operators on Banach spaces. It states that a bijective bounded linear operator T from one Banach space to another has bounded inverse T −1. It is equivalent… …   Wikipedia

  • Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… …   Wikipedia

  • Robertson–Seymour theorem — In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem[1]) states that the undirected graphs, partially ordered by the graph minor relationship, form a well quasi ordering.[2] Equivalently, every family of graphs that …   Wikipedia

  • Minor (graph theory) — In graph theory, an undirected graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained by zero or more edge contractions on a subgraph of G. The theory of graph minors began with Wagner s theorem that a graph… …   Wikipedia


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