Abstract
We study the structure of injective operator spaces and the existence and uniqueness of the injective envelopes of operator spaces. We give an easy example of an injective operator space which is not completely isometric to any C-algebra. This answers a question of Wittstock [23]. Furthermore, we show that an operator space E is injective if and only if there exists an injective C-algebra A and two projections p and q in A such that E is completely isometric to pAq.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 89-104 |
| Number of pages | 16 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 315 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 1989 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics