Statements (64)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
data analysis
functional programming signal processing optimization problems numerical analysis normed vector spaces |
| gptkbp:has_programs |
gptkb:political_movement
|
| https://www.w3.org/2000/01/rdf-schema#label |
Banach-Alaoglu theorem
|
| gptkbp:is_aresource_for |
gptkb:physicist
abstract algebra functional analysis |
| gptkbp:is_cited_in |
gptkb:academic_journal
research papers mathematical literature dissertations textbooks on topology |
| gptkbp:is_connected_to |
nonlinear analysis
convex analysis topological vector spaces measure spaces weak topology |
| gptkbp:is_described_as |
weak* compactness in dual spaces
|
| gptkbp:is_discussed_in |
advanced mathematics courses
conferences on mathematics lectures on functional analysis mathematical analysis textbooks seminars on functional analysis |
| gptkbp:is_essential_for |
functional equations
the study of topological groups the study of convergence in functional analysis the study of linear functional the study of reflexive spaces |
| gptkbp:is_fundamental_to |
theory of distributions
the study of duality in analysis the study of weakly compact sets the study of weakly convergent sequences theory of weak convergence |
| gptkbp:is_related_to |
topological properties
functional spaces sequential compactness Banach space dual space weak convergence bounded linear operators compact operators Hahn-Banach theorem |
| gptkbp:is_tested_for |
topological methods
|
| gptkbp:is_used_in |
functional analysis
theory of distributions theory of convex sets theory of Banach spaces theory of Hilbert spaces theory of linear spaces the study of linear operators theory of Sobolev spaces |
| gptkbp:named_after |
gptkb:Stefan_Banach
Alaoglu |
| gptkbp:state |
the closed unit ball in the dual space is weak* compact
|
| gptkbp:was_akey_figure_in |
functional analysis
topological vector spaces theory of weakly sequentially compact sets |
| gptkbp:bfsParent |
gptkb:Topological_Vector_Spaces
|
| gptkbp:bfsLayer |
6
|