The Banach-Steinhaus Theorem in Abstract Duality Pairs
Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of Fi and l...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2015
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oai:scielo:S0716-091720150004000072016-10-25The Banach-Steinhaus Theorem in Abstract Duality PairsCho,Min-HyungLi,RongluSwartz,CharlesLet E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of Fi and let τFi(Ei) = τi be the topology on Ei of uniform convergence on the members of Fi. Let J be a family of mappings from Ei to E2. We consider conditions which guarantee that J is τ1-τ2equicontinuous. We then apply the results to obtain versions of the Banach-Steinhaus Theorem for both abstract triples and for linear operators between locally convex spaces.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.34 n.4 20152015-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000400007en10.4067/S0716-09172015000400007 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| description |
Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of Fi and let τFi(Ei) = τi be the topology on Ei of uniform convergence on the members of Fi. Let J be a family of mappings from Ei to E2. We consider conditions which guarantee that J is τ1-τ2equicontinuous. We then apply the results to obtain versions of the Banach-Steinhaus Theorem for both abstract triples and for linear operators between locally convex spaces. |
| author |
Cho,Min-Hyung Li,Ronglu Swartz,Charles |
| spellingShingle |
Cho,Min-Hyung Li,Ronglu Swartz,Charles The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| author_facet |
Cho,Min-Hyung Li,Ronglu Swartz,Charles |
| author_sort |
Cho,Min-Hyung |
| title |
The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| title_short |
The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| title_full |
The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| title_fullStr |
The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| title_full_unstemmed |
The Banach-Steinhaus Theorem in Abstract Duality Pairs |
| title_sort |
banach-steinhaus theorem in abstract duality pairs |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2015 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000400007 |
| work_keys_str_mv |
AT chominhyung thebanachsteinhaustheoreminabstractdualitypairs AT lironglu thebanachsteinhaustheoreminabstractdualitypairs AT swartzcharles thebanachsteinhaustheoreminabstractdualitypairs AT chominhyung banachsteinhaustheoreminabstractdualitypairs AT lironglu banachsteinhaustheoreminabstractdualitypairs AT swartzcharles banachsteinhaustheoreminabstractdualitypairs |
| _version_ |
1718439809640300544 |