Banach space
Noun
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Noun
Banach space (plural Banach spaces)
- (functional analysis) A normed vector space which is complete with respect to the norm, meaning that Cauchy sequences have well-defined limits that are points in the space.
- 1962 [Prentice-Hall], Kenneth Hoffman, Banach Spaces of Analytic Functions, 2007, Dover, page 138 ↗,
- Before taking up the extreme points for H^1 and H^\infty, let us make a few elementary observations about the unit ball \Sigma in the Banach space X.
- 1992, R. M. Dudley, M. G. Hahn, James Kuelbs (editors), Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference, Springer, page ix ↗,
- Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonseparable.
- 2013, R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, page 35 ↗,
- [A] Banach space is a complete normed linear space X. Its dual space X' is the linear space of all continuous linear functionals f : X \rightarrow\mathbb{R}, and it has norm \left\Vert f\right\|_{X'}\equiv \text{sup}\left\{\left\vert f(x)\right\vert : \left\Vert x\right\Vert \le 1\right\}; X' is also a Banach space.
- 1962 [Prentice-Hall], Kenneth Hoffman, Banach Spaces of Analytic Functions, 2007, Dover, page 138 ↗,
- French: espace de Banach
- German: Banach-Raum
- Italian: spazio di Banach
- Russian: ба́нахово простра́нство
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.005