d-independence and d-bases in vector lattices
| dc.creator | Abramovich, Y. A. | |
| dc.creator | Kitover, A. K. | |
| dc.date | 1999-03-26 | |
| dc.date.accessioned | 2026-07-07T05:28:29Z | |
| dc.date.available | 2026-07-07T05:28:29Z | |
| dc.description | This article contains the results of two types. First we give a complete characterization of band preserving projection operators on Dedekind complete vector lattices. This is done in Theorem~3.4. Let us mention also Theorem~3.2 that contains a description of such operators on arbitrary laterally complete vector lattices. The central role in these descriptions is played by d-bases, one of two principal tools utilized in our work [{\it Inverses of Disjointness Preserving Operators}, Memoirs of the Amer. Math. Soc., forthcoming]. The concept of a d-basis has been applied so far only to vector lattices with a large amount of projection bands. The absence of the projection bands has been the major obstacle for extending, otherwise very useful concept of d-bases, to arbitrary vector lattices. In Section~4 we overcome this obstacle by finding a new way to introduce d-independence in an arbitrary vector lattice. This allows us to produce a new definition of a d-basis which is free of the existence of projection bands. We illustrate this by proving several results devoted to cardinality of d-bases. Theorems~4.13 and~4.15 are the main of them and they assert that, under very general conditions, a vector lattice either has a singleton d-basis of else this d-basis must be infinite. | |
| dc.description | 15 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9903156 | |
| dc.identifier | http://arxiv.org/abs/math/9903156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78275 | |
| dc.subject | Functional Analysis | |
| dc.subject | 47B60; 47B65; 46A40 | |
| dc.title | d-independence and d-bases in vector lattices | |
| dc.type | text |