The complete separable extension property
| dc.creator | Rosenthal, Haskell P. | |
| dc.date | 1998-04-14 | |
| dc.date.accessioned | 2026-07-07T05:24:23Z | |
| dc.date.available | 2026-07-07T05:24:23Z | |
| dc.description | This work introduces operator space analogues of the Separable Extension Property (SEP) for Banach spaces; the Complete Separable Extension Property (CSEP) and the Complete Separable Complemention Property (CSCP). The results use the technique of a new proof of Sobczyk's Theorem, which also yields new results for the SEP in the non-separable situation, e.g., $(\oplus_{n=1}^\infty Z_n)_{c_0}$ has the $(2+\ep)$-SEP for all $\ep>0$ if $Z_1,Z_2,...$ have the 1-SEP; in particular, $c_0 (\ell^\infty)$ has the SEP. It is proved that e.g., $c_0(\bR\oplus\bC)$ has the CSEP (where $\bR$, $\bC$ denote Row, Column space respectively) as a consequence of the general principle: if $Z_1,Z_2,...$ is a uniformly exact sequence of injective operator spaces, then $(\oplus_{n=1}^\infty Z_n)_{c_0}$ has the CSEP. Similarly, e.g., $\bK_0 \defeq (\oplus_{n=1}^\infty M_n)_{c_0}$ has the CSCP, due to the general principle: $(\oplus_{n=1}^\infty Z_n)_{c_0}$ has the CSCP if $Z_1,Z_2,...$ are injective separable operator spaces. Further structural results are obtained for these properties, and several open problems and conjectures are discussed. | |
| dc.description | 56 pages | |
| dc.identifier | https://arxiv.org/abs/math/9804064 | |
| dc.identifier | http://arxiv.org/abs/math/9804064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76821 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B15, 47D25 | |
| dc.title | The complete separable extension property | |
| dc.type | text |