Weak type $(2,H)$ and weak cotype $(2,H)$ of operator spaces
| dc.creator | Lee, Hun Hee | |
| dc.date | 2005-02-16 | |
| dc.date | 2007-07-02 | |
| dc.date.accessioned | 2026-07-07T08:13:13Z | |
| dc.date.available | 2026-07-07T08:13:13Z | |
| dc.description | Recently an operator space version of type and cotype, namely type $(p,H)$ and cotype $(q,H)$ of operator spaces for $1\leq p \leq 2\leq q \leq \infty$ and a subquadratic and homogeneous Hilbetian operator space $H$ were introduced and investigated by the author. In this paper we define weak type $(2,H)$ (resp. weak cotype $(2,H)$) of operator spaces, which lies strictly between type $(2,H)$ (resp. cotype $(2,H)$) and type $(p,H)$ for all $1\leq p <2$ (resp. cotype $(q,H)$ for all $2<q \leq \infty$). This is an analogue of weak type 2 and weak cotype 2 in the Banach space case, so we develop analogous equivalent formulations. We also consider weak-$H$ space, spaces with weak type $(2,H)$ and weak cotype $(2,H^*)$ simultaneously and establish corresponding equivalent formulations. | |
| dc.description | 22 pages, Definition is broadened, and eigen value estimation for weak $H$-space has been added. Tsirelson type construction is removed | |
| dc.identifier | https://arxiv.org/abs/math/0502337 | |
| dc.identifier | http://arxiv.org/abs/math/0502337 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132722 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 47L25; 46B07 | |
| dc.title | Weak type $(2,H)$ and weak cotype $(2,H)$ of operator spaces | |
| dc.type | text |