Mathematics – Operator Algebras
Scientific paper
1999-10-21
Int. Math. J. 1(2002), no. 6, 611-620
Mathematics
Operator Algebras
10 pages, LaTeX2e, one statement and its proof corrected
Scientific paper
The local multiplier C*-algebra M_{loc}(A) of any C*-algebra A can *-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 M_{loc}(A) = I(A) . The injective envelopes of A and M_{loc}(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the regular monotone completion \bar{A} in I(A) of A . In case the set Z(A).A is dense in A the center of the local multiplier C*-algebra of A is the local multiplier C*-algebra of the center of A, and both they are *-isomorphic to the injective envelope of the center of A . A Wittstock type extension theorem for completely bounded bimodule maps on operator bimodules taking values in M_{loc}(A) is proven to hold if and only if M_{loc}(A) = I(A). In general, a solution of the problem for which C*-algebras A the C*-algebras M_{loc}(A) is injective is shown to be equivalent to the solution of I. Kaplansky's 1951 problem whether all AW*-algebras are monotone complete.
Frank Michael
No associations
LandOfFree
Injective envelopes and local multiplier algebras of C*-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Injective envelopes and local multiplier algebras of C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Injective envelopes and local multiplier algebras of C*-algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-250384