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Statements

Subject Item
dbr:Mackey_topology
rdf:type
yago:WikicatTopologicalVectorSpaces yago:Communication100033020 yago:Proposition106750804 yago:Theorem106752293 yago:Statement106722453 yago:Attribute100024264 yago:WikicatMathematicalTheorems yago:Message106598915 yago:Abstraction100002137 yago:Space100028651
rdfs:label
マッキー位相 Satz von Mackey-Arens Mackey topology Topologia di Mackey
rdfs:comment
函数解析学および関連する数学の分野において、の名にちなむマッキー位相（マッキーいそう、英: Mackey topology）とは、位相線型空間に対する位相で、連続双対を保存するものである。すなわちマッキー位相は、元の位相で不連続である線型函数を連続にすることはない。 マッキー位相は、連続双対において全ての連続函数の連続性を保存する位相線型空間上の位相である弱位相と反対の概念である。 マッキー＝アレンスの定理では、すべての双対位相は弱位相より細かく、マッキー位相より粗いことが示されている。 In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. A topological vector space (TVS) is called a Mackey space if its topology is the same as the Mackey topology. The Mackey–Arens theorem states that all possible dual topologies are finer than the weak topology and coarser than the Mackey topology. Der Satz von Mackey-Arens (nach George Mackey und Richard Friederich Arens) ist ein mathematischer Satz aus der Funktionalanalysis, genauer aus der Theorie der lokalkonvexen Räume. Der Satz von Mackey-Arens behandelt die Frage, in welchen Topologien bestimmte wichtige Abbildungen stetig sind. Es stellt sich heraus, dass es eine schwächste und eine stärkste zulässige Topologie gibt. In matematica, in particolare in analisi funzionale, la topologia di Mackey o topologia di Arens-Mackey, il cui nome è dovuto a George Mackey, è la topologia più fine per uno spazio vettoriale topologico che preserva il duale continuo. In altri termini, la topologia di Mackey non rende continue funzioni lineari che sono discontinue nella topolgia di default del duale continuo. La topologia di Mackey è l'opposto della topologia debole, che è la topologia più grezza su uno spazio vettoriale topologico che preserva la continuità delle funzioni lineari nel duale continuo.
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dbc:Topological_vector_spaces
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1790627
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1108339176
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dbt:Boundedness_and_bornology dbt:Schaefer_Wolff_Topological_Vector_Spaces dbt:Springer dbt:Reflist dbt:Main dbt:Duality_and_spaces_of_linear_maps dbt:Narici_Beckenstein_Topological_Vector_Spaces dbt:Topological_vector_spaces dbt:Annotated_link dbt:Functional_analysis dbt:Cite_book dbt:Bourbaki_Topological_Vector_Spaces_Part_1_Chapters_1–5 dbt:Cite_journal
dbp:author
A.I. Shtern
dbp:id
M/m062080
dbp:title
Mackey topology
dbo:abstract
In matematica, in particolare in analisi funzionale, la topologia di Mackey o topologia di Arens-Mackey, il cui nome è dovuto a George Mackey, è la topologia più fine per uno spazio vettoriale topologico che preserva il duale continuo. In altri termini, la topologia di Mackey non rende continue funzioni lineari che sono discontinue nella topolgia di default del duale continuo. La topologia di Mackey è l'opposto della topologia debole, che è la topologia più grezza su uno spazio vettoriale topologico che preserva la continuità delle funzioni lineari nel duale continuo. Il afferma che tutte le possibili sono più fini della topologia debole e più grezze della topolgia di Mackey. 函数解析学および関連する数学の分野において、の名にちなむマッキー位相（マッキーいそう、英: Mackey topology）とは、位相線型空間に対する位相で、連続双対を保存するものである。すなわちマッキー位相は、元の位相で不連続である線型函数を連続にすることはない。 マッキー位相は、連続双対において全ての連続函数の連続性を保存する位相線型空間上の位相である弱位相と反対の概念である。 マッキー＝アレンスの定理では、すべての双対位相は弱位相より細かく、マッキー位相より粗いことが示されている。 Der Satz von Mackey-Arens (nach George Mackey und Richard Friederich Arens) ist ein mathematischer Satz aus der Funktionalanalysis, genauer aus der Theorie der lokalkonvexen Räume. Der Satz von Mackey-Arens behandelt die Frage, in welchen Topologien bestimmte wichtige Abbildungen stetig sind. Genauer sei ein lokalkonvexer Raum mit einer Topologie gegeben. Dann betrachtet man den Dualraum E' der bezüglich stetigen, linearen Funktionale auf . Die Frage ist nun, welche weiteren lokalkonvexen Topologien auf zu denselben stetigen, linearen Funktionalen wie führen. Solche Topologien heißen zulässig. Es stellt sich heraus, dass es eine schwächste und eine stärkste zulässige Topologie gibt. In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. A topological vector space (TVS) is called a Mackey space if its topology is the same as the Mackey topology. The Mackey topology is the opposite of the weak topology, which is the coarsest topology on a topological vector space which preserves the continuity of all linear functions in the continuous dual. The Mackey–Arens theorem states that all possible dual topologies are finer than the weak topology and coarser than the Mackey topology.
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dbr:Topology
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