ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES

ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES

Mostrar otras versiones (1)

Let X, Y be locally convex spaces and L(X, Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series sigmaTk in L(X, Y ). First, if lambda is a scalar sequence space, we say that the series sigmaTk is lambda multiplier convergent...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: SWARTZ,CHARLES
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2004
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000100005
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
id oai:scielo:S0716-09172004000100005
record_format dspace
spelling oai:scielo:S0716-091720040001000052004-06-08ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIESSWARTZ,CHARLESLet X, Y be locally convex spaces and L(X, Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series sigmaTk in L(X, Y ). First, if lambda is a scalar sequence space, we say that the series sigmaTk is lambda multiplier convergent for a locally convex topology tau on L(X, Y ) if the series sigmat kTk is tau convergent for every t = {t k} <FONT FACE=Symbol>Î</FONT>lambda . We establish conditions on &#955; which guarantee that a &#955; multiplier convergent series in the weak or strong operator topology is lambda multiplier convergent in the topology of uniform convergence on the bounded subsets of X. Second, we consider vector valued multipliers. If E is a sequence space of X valued sequences, the series sigmaTk is E multiplier convergent in a locally convex topology eta on Y if the series sigmaTk x k is &#951; convergent for every x = {xk} <FONT FACE=Symbol>Î</FONT> E. We consider a gliding hump property on E which guarantees that a series sigmaTk which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Yinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.23 n.1 20042004-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000100005en10.4067/S0716-09172004000100005
institution Scielo Chile
collection Scielo Chile
language English
description Let X, Y be locally convex spaces and L(X, Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series sigmaTk in L(X, Y ). First, if lambda is a scalar sequence space, we say that the series sigmaTk is lambda multiplier convergent for a locally convex topology tau on L(X, Y ) if the series sigmat kTk is tau convergent for every t = {t k} <FONT FACE=Symbol>Î</FONT>lambda . We establish conditions on &#955; which guarantee that a &#955; multiplier convergent series in the weak or strong operator topology is lambda multiplier convergent in the topology of uniform convergence on the bounded subsets of X. Second, we consider vector valued multipliers. If E is a sequence space of X valued sequences, the series sigmaTk is E multiplier convergent in a locally convex topology eta on Y if the series sigmaTk x k is &#951; convergent for every x = {xk} <FONT FACE=Symbol>Î</FONT> E. We consider a gliding hump property on E which guarantees that a series sigmaTk which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Y
author SWARTZ,CHARLES
spellingShingle SWARTZ,CHARLES
ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
author_facet SWARTZ,CHARLES
author_sort SWARTZ,CHARLES
title ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
title_short ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
title_full ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
title_fullStr ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
title_full_unstemmed ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES
title_sort orlicz - pettis theorems for multiplier convergent operator valued series
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2004
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172004000100005
work_keys_str_mv AT swartzcharles orliczpettistheoremsformultiplierconvergentoperatorvaluedseries
_version_ 1718439734877880320

Ejemplares similares