GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM

GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM

The Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the te...

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Autores principales: STUART,CHRISTOPHER, SWARTZ,CHARLES
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2005
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100004
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spelling oai:scielo:S0716-091720050001000042005-07-06GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREMSTUART,CHRISTOPHERSWARTZ,CHARLESThe Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the terms of the series are multiplied by elements of the scalar sequence space m0 of sequences with finite range. In this paper we show that the conclusion of the Orlicz-Pettis Theorem holds (and can be strengthened) if the multiplier space m0 is replaced by a sequence space with the signed weak gliding hump propertyinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.24 n.1 20052005-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100004en10.4067/S0716-09172005000100004
institution Scielo Chile
collection Scielo Chile
language English
description The Orlicz-Pettis Theorem for locally convex spaces asserts that a series in the space which is subseries convergent in the weak topology is actually subseries convergent in the original topology of the space. A subseries convergent series can be viewed as a multiplier convergent series where the terms of the series are multiplied by elements of the scalar sequence space m0 of sequences with finite range. In this paper we show that the conclusion of the Orlicz-Pettis Theorem holds (and can be strengthened) if the multiplier space m0 is replaced by a sequence space with the signed weak gliding hump property
author STUART,CHRISTOPHER
SWARTZ,CHARLES
spellingShingle STUART,CHRISTOPHER
SWARTZ,CHARLES
GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
author_facet STUART,CHRISTOPHER
SWARTZ,CHARLES
author_sort STUART,CHRISTOPHER
title GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
title_short GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
title_full GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
title_fullStr GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
title_full_unstemmed GENERALIZATIONS OF THE ORLICZ-PETTIS THEOREM
title_sort generalizations of the orlicz-pettis theorem
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2005
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100004
work_keys_str_mv AT stuartchristopher generalizationsoftheorliczpettistheorem
AT swartzcharles generalizationsoftheorliczpettistheorem
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