Kadec-Pelczynski decomposition for Haagerup L_p-spaces
| dc.creator | Randrianantoanina, Narcisse | |
| dc.date | 2000-02-02 | |
| dc.date.accessioned | 2026-07-07T04:33:33Z | |
| dc.date.available | 2026-07-07T04:33:33Z | |
| dc.description | Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pelczynski subsequence decomposition of bounded sequences in L^p[0,1] to the case of the Haagerup L^p-spaces (1\le p<\infty). In particular, we prove that if (ϕ_n)_n is a bounded sequence in the predual M_* of M, then there exist a subsequence (ϕ_{n_k})_k of (ϕ_n)_n, a decomposition ϕ_{n_k}= y_k+ z_k such that {y_k, k\ge 1} is relatively weaklycompact and the support projections s(z_k)\downarrow_k 0 (or similarly mutually disjoint). As an application, we prove that every non-reflexive subspace of the dual of any given C*-algebra (or Jordan triples) contains asymptotically isometric copies of l_1 and therefore fails the fixed point property for nonexpansive mappings. These generalize earlier results for the case of preduals of semi-finite von Neumann algebras. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002016 | |
| dc.identifier | http://arxiv.org/abs/math/0002016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58615 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L50;47D15 | |
| dc.title | Kadec-Pelczynski decomposition for Haagerup L_p-spaces | |
| dc.type | text |