Corollary 1 says that if $f$ is a bounded linear functional defined on a subspace $Y$ of a normed linear space $X$ then $f$ can be extended to a bounded linear ...

It allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space, and it also shows that there are " ... History · Continuous extension theorem · Generalizations

7 июл. 2016 г. · A corollary of the Hahn-Banach theorem ... Let Z be a subspace of normed linear space X and that y is an element of X whose distance from Z is d. Corollary of the Hahn Banach theorem - Math Stack Exchange Corollary of Hahn-Banach theorem regarding the norm Corollary of Hahn-Banach - Math Stack Exchange Corollary of the Hahn-Banach theorem. Другие результаты с сайта math.stackexchange.com

The hyperplane separation theorem says that two convex sets where one of them has an interior point can be separated by a hyperplane. This is a corollary of the ...

Corollary 6.7 Let X be a normed linear space. Every proper closed linear subspace M ⊂ X is the intersection of the closed hyperplanes containing it. Why does ...

21 сент. 2018 г. · Corollary 7 Let V be a normed vector space, Y be a subspace of V and x ∈V\Y with the distance from x to Y being d. There is a Λ ∈ V∗ such that ...

Corollary 2.12. The statement of Theorem 2.11 is true in particular if X is a. Banach space and E = X (any Banach space is of 2nd category) ...

The theorem guarantees that every continuous linear functional on a subspace can be extended to the whole space with norm conservation. 1 Hahn-Banach theorems.

1 мая 2017 г. · Corollary 14.8. Let X be a normed linear space. If X0 is a finite dimensional subspace of X, then there is a closed linear subspace X1 of X.

Corollary 3.3. Let A and B be nonempty disjoint convex subsets of a real normed linear space X. Suppose A is compact and B is closed.