UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES

dc.creator	SWARTZ,CHARLES
dc.date	2004-12-01
dc.date.accessioned	2020-02-17T15:34:16Z
dc.date.available	2020-02-17T15:34:16Z
dc.identifier	https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000300003
dc.identifier.uri	https://revistaschilenas.uchile.cl/handle/2250/131231
dc.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}
dc.format	text/html
dc.language	en
dc.publisher	Universidad Católica del Norte, Departamento de Matemáticas
dc.relation	10.4067/S0716-09172004000300003
dc.rights	info:eu-repo/semantics/openAccess
dc.source	Proyecciones (Antofagasta) v.23 n.3 2004
dc.title	UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES