A dichotomy property for locally compact groups
Ver/ Abrir
Impacto
Scholar |
Otros documentos de la autoría: Ferrer González, María Vicenta; Hernández, Salvador; Tárrega Ruiz, Luis
Metadatos
Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
A dichotomy property for locally compact groupsFecha de publicación
2018-08Editor
ElsevierCita bibliográfica
FERRER, María V.; HERNÁNDEZ, Salvador; TÁRREGA, Luis. A dichotomy property for locally compact groups. Journal of Functional Analysis, 2018, 275.4: 869-891.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0022123618301228Versión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of l1. For that purpose, we transfer to general locally compact groups the notion of interpolation ... [+]
We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of l1. For that purpose, we transfer to general locally compact groups the notion of interpolation (Io) set, which was defined by Hartman and Ryll-Nardzewsky for locally compact abelian groups. Thus we prove that for every sequence [gn]n<w in a locally compact group G, then either [gn]n<w has a weak Cauchy subsequence or contains a subsequence that is an Io set. This result is subsequently applied to obtain sufficient conditions for the existence of Sidon sets in a locally compact group G, an old question that remains open since 1974. Finally, we show that every locally compact group strongly respects compactness extending thereby a result by Comfort, Trigos-Arrieta, and Wu [13], who established this property for abelian locally compact groups. [-]
Proyecto de investigación
Spanish Ministerio de Economía y Competitividad, grant MTM2016-77143-P (AEI/FEDER, EU) ; Universitat Jaume I (grant P1171B2015-77) ; Generalitat Valenciana (PROMETEO/2014/062)Derechos de acceso
© 2018 Elsevier Inc. All rights reserved.
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
Aparece en las colecciones
- INIT_Articles [743]
- IMAC_Articles [119]
- MAT_Articles [749]