منابع مشابه
Separably Injective Banach Spaces
It is no exaggeration to say that the theory of separably injective spaces is quite different from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in the main topic of the monograph, namely, separably injective spaces and their “universal” version. After giving the main definitions and taking a look at the first natural examples one encounters, we presen...
متن کاملSeparably Injective Banach Spaces
It is no exaggeration to say that the theory of separably injective spaces is quite different from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in the main topic of the monograph, namely, separably injective spaces and their “universal” version. After giving the main definitions and taking a look at the first natural examples one encounters, we presen...
متن کاملInjective Hulls of C* Algebras. Ii
Proof. The idempotents correspond to the Borel sets modulo sets of first category. Since, in addition, the idempotents generate B(X), B(X) is an AW* and hence an injective algebra. The natural map U of C(X) into B(X) induced by the inclusion map is clearly a homomorphism. It is one-one since continuous functions which are not identically equal must differ on a set of second category. To complet...
متن کاملInjective Envelopes of Separable C * -algebras
Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...
متن کاملInjective Envelopes and Local Multiplier Algebras of C*-algebras
The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2016
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-016-0905-3