ar X iv : m at h / 01 06 13 1 v 1 [ m at h . O A ] 1 5 Ju n 20 01 INJECTIVE ENVELOPES OF C ∗ - ALGEBRAS AS OPERATOR MODULES
نویسنده
چکیده
In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yields a natural representation of many kinds of multipliers as multiplications by elements of I(A). In particular, we prove that the(n times iterated) local multiplier algebra of A embeds into I(A).
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