 
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 downwarddirected 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
