Statements (66)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:collection
|
| gptkbp:defines |
Complete normed vector space
|
| gptkbp:has |
L^p spaces for 1 ≤ p < ∞
Sequence spaces like l^p Continuous functions on a closed interval The space of bounded functions |
| gptkbp:has_method |
gptkb:Banach-Alaoglu_theorem
Open Mapping Theorem Hahn-Banach theorem Banach-Steinhaus theorem Closed Graph Theorem Uniform Boundedness Principle |
| gptkbp:has_programs |
gptkb:political_movement
Signal Processing Applied Mathematics Control Theory |
| gptkbp:has_property |
Can be equipped with different norms
Can be normed by different metrics Can be reflexive or non-reflexive Can be separable or non-separable Can be used in applied physics Can be used in approximation algorithms Can be used in approximation theory Can be used in computational mathematics Can be used in computer graphics Can be used in control systems Can be used in data analysis Can be used in differential equations Can be used in economics Can be used in engineering Can be used in functional equations Can be used in game theory Can be used in image processing Can be used in integral equations Can be used in machine learning Can be used in network theory Can be used in numerical analysis Can be used in optimization algorithms Can be used in optimization problems Can be used in robotics Can be used in signal reconstruction Can be used in statistics Can be used in stochastic processes Can be used in theoretical physics Can be used in variational methods Can be used to study continuity of functions Can be used to study convergence of sequences Can be used to study fixed point theorems Can be used to study linear transformations Completeness is a key feature Contains all Cauchy sequences Dual space exists Every closed subspace is a Banach space Every continuous linear functional is bounded Has a topology induced by the norm Is a generalization of Euclidean spaces Norm is a measure of size Vector space over the field of real or complex numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
Banach Spaces
|
| gptkbp:length |
Can be finite or infinite dimensional
|
| gptkbp:named_after |
gptkb:Stefan_Banach
|
| gptkbp:related_to |
Hilbert Spaces
Linear Operators |
| gptkbp:used_in |
Functional Analysis
|
| gptkbp:bfsParent |
gptkb:Topological_Vector_Spaces
|
| gptkbp:bfsLayer |
6
|