Embeddings of Banach Spaces into Banach Lattices and the Gordon-Lewis Property
| dc.creator | Casazza, Peter G. | |
| dc.creator | Nielsen, N. J. | |
| dc.date | 1998-12-30 | |
| dc.date.accessioned | 2026-07-07T05:27:24Z | |
| dc.date.available | 2026-07-07T05:27:24Z | |
| dc.description | In this paper we first show that if $X$ is a Banach space and $α$ is a left invariant crossnorm on $\ell_\infty\otimes X$, then there is a Banach lattice $L$ and an isometric embedding $J$ of $X$ into $L$, so that $I\otimes J$ becomes an isometry of $\ell_\infty\otimes_αX$ onto $\ell_\infty\otimes_m J(X)$. Here $I$ denotes the identity operator on $\ell_\infty$ and $\ell_\infty\otimes_m J(X)$ the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to characterize the Gordon-Lewis property $\GL$ in terms of embeddings into Banach lattices. Also other structures related to the $\GL$ are investigated. | |
| dc.description | 32 pages, latex2e | |
| dc.identifier | https://arxiv.org/abs/math/9812160 | |
| dc.identifier | http://arxiv.org/abs/math/9812160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77906 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B40; 46B42 | |
| dc.title | Embeddings of Banach Spaces into Banach Lattices and the Gordon-Lewis Property | |
| dc.type | text |