Mostrar el registro sencillo del ítem
dc.contributor.author | Okada, S. | es_ES |
dc.contributor.author | Ricker, W. J. | es_ES |
dc.contributor.author | Sánchez Pérez, Enrique Alfonso | es_ES |
dc.date.accessioned | 2016-01-29T08:47:10Z | |
dc.date.available | 2016-01-29T08:47:10Z | |
dc.date.issued | 2014 | |
dc.identifier.issn | 0012-3862 | |
dc.identifier.uri | http://hdl.handle.net/10251/60348 | |
dc.description.abstract | The spaces L1(m) of all m-integrable (resp. L1w(m) of all scalarly m-integrable) functions for a vector measure m, taking values in a complex locally convex Hausdorff space X (briefly, lcHs), are themselves lcHs for the mean convergence topology. Additionally, L1w(m) is always a complex vector lattice; this is not necessarily so for L1(m). To identify precisely when L1(m) is also a complex vector lattice is one of our central aims. Whenever X is sequentially complete, then this is the case. If, additionally, the inclusion L1(m) in L1w(m) (which always holds) is proper, then L1(m) and L1w(m) contain lattice-isomorphic copies of the complex Banach lattices c0 and `1, respectively. On the other hand, whenever L1(m) contains an isomorphic copy of c0, merely in the lcHs sense, then necessarily L1(m) ( L1w(m). Moreover, the X-valued integration operator Im, then fixes a copy of c0. For X a Banach space, the validity of L1(m) = L1w(m) turns out to be equivalent to Im being weakly completely continuous. A sufficient condition for this is the (q; 1)-concavity of Im for some q . This criterion is fulfilled when Im belongs to various classical operator ideals. Unlike for L1w(m), the space L1(m) can never contain an isomorphic copy of l infinity. A rich supply of examples and counterexamples is presented. The methods involved are a hybrid of vector measure/integration theory, functional analysis, operator theory and complex vector lattices. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Polish Academy od Sciences. Institute of Matematics | es_ES |
dc.relation.ispartof | Dissertationes Mathematicae | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Vector measure | es_ES |
dc.subject | Space of integrable functions | es_ES |
dc.subject | Integration operator | es_ES |
dc.subject | Locally convex space | es_ES |
dc.subject | Complex vector lattice | es_ES |
dc.subject | Operator ideal | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Lattice copies of c(0) and l infinity in spaces of integrable functions for a vector measure | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.4064/dm500-0-1 | |
dc.rights.accessRights | Cerrado | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada | es_ES |
dc.description.bibliographicCitation | Okada, S.; Ricker, WJ.; Sánchez Pérez, EA. (2014). Lattice copies of c(0) and l infinity in spaces of integrable functions for a vector measure. Dissertationes Mathematicae. 500:1-68. doi:10.4064/dm500-0-1 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | http://dx.doi.org/10.4064/dm500-0-1 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 68 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 500 | es_ES |
dc.relation.senia | 279014 | es_ES |