Weakly compact approximation in Banach spaces
| dc.creator | Odell, Edward | |
| dc.creator | Tylli, Hans-Olav | |
| dc.date | 2003-09-24 | |
| dc.date.accessioned | 2026-07-07T05:01:25Z | |
| dc.date.available | 2026-07-07T05:01:25Z | |
| dc.description | The Banach space $E$ has the weakly compact approximation property (W.A.P. for short) if there is a constant $C < \infty$ so that for any weakly compact set $D \subset E$ and $ε> 0$ there is a weakly compact operator $V: E \to E$ satisfying $\sup_{x\in D} || x - Vx || < ε$ and $|| V|| \leq C$. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type spaces from a general class of quasi-reflexive spaces (which contains the classical James' space $J$) have the W.A.P, but that James' tree space $JT$ fails to have the W.A.P. It is also shown that the dual $J^*$ has the W.A.P. It follows that the Banach algebras $W(J)$ and $W(J^*)$, consisting of the weakly compact operators, have bounded left approximate identities. Among the other results we obtain a concrete Banach space $Y$ so that $Y$ fails to have the W.A.P., but $Y$ has this approximation property without the uniform bound $C$. | |
| dc.description | 39 pages, plain tex document | |
| dc.identifier | https://arxiv.org/abs/math/0309405 | |
| dc.identifier | http://arxiv.org/abs/math/0309405 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68664 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B28 | |
| dc.title | Weakly compact approximation in Banach spaces | |
| dc.type | text |