UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES
Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences chi = {<FONT FACE=Symbol>c k</FONT>} such that...
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Universidad Católica del Norte, Departamento de Matemáticas
2004
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oai:scielo:S0716-091720040003000032005-02-03UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACESSWARTZ,CHARLESLet µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences chi = {<FONT FACE=Symbol>c k</FONT>} such that {q(<FONT FACE=Symbol>c k</FONT>)} <FONT FACE=Symbol>Î</FONT>µ{X} for all q <FONT FACE=Symbol>Î</FONT> X. The space µ{X} is given the locally convex topology generated by the semi-norms <FONT FACE=Symbol>ðp</FONT>pq(chi) = p({q(<FONT FACE=Symbol>c k</FONT>)}), p <FONT FACE=Symbol>Î</FONT> X, q <FONT FACE=Symbol>Î</FONT> M. We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the â-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.23 n.3 20042004-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000300003en10.4067/S0716-09172004000300003 |
| institution |
Scielo Chile |
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Scielo Chile |
| language |
English |
| description |
Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences chi = {<FONT FACE=Symbol>c k</FONT>} such that {q(<FONT FACE=Symbol>c k</FONT>)} <FONT FACE=Symbol>Î</FONT>µ{X} for all q <FONT FACE=Symbol>Î</FONT> X. The space µ{X} is given the locally convex topology generated by the semi-norms <FONT FACE=Symbol>ðp</FONT>pq(chi) = p({q(<FONT FACE=Symbol>c k</FONT>)}), p <FONT FACE=Symbol>Î</FONT> X, q <FONT FACE=Symbol>Î</FONT> M. We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the â-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X} |
| author |
SWARTZ,CHARLES |
| spellingShingle |
SWARTZ,CHARLES UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| author_facet |
SWARTZ,CHARLES |
| author_sort |
SWARTZ,CHARLES |
| title |
UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| title_short |
UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| title_full |
UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| title_fullStr |
UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| title_full_unstemmed |
UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES |
| title_sort |
uniform boundedness in vector - valued sequence spaces |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2004 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000300003 |
| work_keys_str_mv |
AT swartzcharles uniformboundednessinvectorvaluedsequencespaces |
| _version_ |
1718439738296238080 |