Injectivity of Operator Spaces
Copyright policy )Injectivity of Operator Spaces
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 ∗ {C^\ast } -algebra. This answers a question of Wittstock [23]. Furthermore, we show that an operator space E E is injective if and only if there exists an injective C ∗ {C^\ast } -algebra A A and two projections p p and q q in A A such that E E is completely isometric to p A q pAq .
- University of Illinois at Urbana Champaign United States
- University of California, Berkeley United States
- University of Illinois System United States
General theory of \(C^*\)-algebras, injective operator spaces, existence and uniqueness of the injective envelopes of operator spaces, injective \(C^*\)-algebra
General theory of \(C^*\)-algebras, injective operator spaces, existence and uniqueness of the injective envelopes of operator spaces, injective \(C^*\)-algebra
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