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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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2004
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000300003 |
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| Sumario: | 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} |
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