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Summary: LOCAL MULTIPLIER ALGEBRAS, INJECTIVE ENVELOPES,
AND TYPE I W
-ALGEBRAS
MART´IN ARGERAMI AND DOUGLAS R. FARENICK
Abstract. Characterizations of those separable C
-algebras that have W
-algebra
injective envelopes or W
-algebra local multiplier algebras are presented. The C
-
envelope and the injective envelope of a class of operator systems that generate
certain type I von Neumann algebras are also determined.
The local multiplier algebra Mloc(A) of a C
-algebra A is the C
-algebraic direct
limit of multiplier algebras M(K) along the downward-directed system E(A) of all
(closed) essential ideals K of A. Such algebras first arose in the study of derivations
and were formally introduced by Pedersen in [17], where he proves that every deriva-
tion on a separable C
-algebra A extends to an inner derivation of Mloc(A). The
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