About: Dual system

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In mathematics, a dual system, dual pair, or duality over a field is a triple consisting of two vector spaces and over and a non-degenerate bilinear map . Duality theory, the study of dual systems, is part of functional analysis. According to Helmut H. Schaefer, "the study of a locally convex space in terms of its dual is the central part of the modern theory of topological vector spaces, for it provides the deepest and most beautiful results of the subject."

Attributes	Values
rdf:type	Thing
rdfs:label	Dual system (en)
rdfs:comment	In mathematics, a dual system, dual pair, or duality over a field is a triple consisting of two vector spaces and over and a non-degenerate bilinear map . Duality theory, the study of dual systems, is part of functional analysis. According to Helmut H. Schaefer, "the study of a locally convex space in terms of its dual is the central part of the modern theory of topological vector spaces, for it provides the deepest and most beautiful results of the subject." (en)
rdfs:seeAlso	Transpose of a linear map
name	Theorem (en) Proposition (en) Mackey's theorem (en) Mackey-Arens theorem I (en) Mackey-Arens theorem II (en) Weak representation theorem (en)
dct:subject	Topological vector spaces Duality theories Functional analysis
Wikipage page ID	63735167 (xsd:integer)
Wikipage revision ID	1108334527 (xsd:integer)
Link from a Wikipage to another Wikipage	Metrizable space Topological embedding Barrelled space Bounded set (topological vector space) Degenerate bilinear form Topological vector spaces Vector space Complete topological vector space Complex conjugate vector space Complex number Continuous dual space Continuous linear functional Mathematics Orthonormal Separable space Duality theories Equicontinuity Equicontinuous Locally convex topological vector space Strong dual topology Comparison of topologies Functional analysis Helmut H. Schaefer Annihilator (linear algebra) Polar set Mackey space Mackey topology Balanced set Banach space Topological vector space Totally bounded Weak-* topology Weak topology Dual basis Hausdorff space Absolutely convex set Field (mathematics) Directed set Hermitian adjoint Hilbert space Absorbing set Functional analysis Bilinear map Bipolar theorem Polar topology Metrizable TVS Injective function Neighborhood basis Net (mathematics) Open map Orthogonal complement Real number Real polar Reflexive space Semi-reflexive space Sequence space Sesquilinear Without loss of generality Locally convex Subspace topology Sesquilinear form Strong dual space Barreled space Mackey-Arens theorem Bidual Algebraic dual space Polar topologies Quotient topology Conjugate homogeneous Injective map Beta dual Pre-Hilbert space Subbasis
Link from a Wikipage to an external page	http://www.math.uh.edu/~hjm/vol18-3.html%7Cjournal https://www.math.ksu.edu/~nagy/func-an-2007-2008/dt-1.pdf
sameAs	Dual system Dual system
dbp:wikiPageUsesTemplate	dbt:' dbt:About dbt:Anchor dbt:Annotated_link dbt:Cite_journal dbt:Em dbt:ISBN dbt:Main

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