Full extensions and approximate unitary equivalences

Details Full extensions and approximate unitary equivalences Full extensions and approximate unitary equivalences

2004-01-19

arxiv.org/abs/math/0401242v1

Mathematics

Operator Algebras

Scientific paper

Let $A$ be a unital separable amenable \CA and $C$ be a unital \CA with certain infinite property. We show that two full monomorphisms $h_1, h_2: A\to C$ are approximately unitarily equivalent if and only if $[h_1]=[h_2]$ in $KL(A,C).$ Let $B$ be a non-unital but $\sigma$-unital \CA for which $M(B)/B$ has the certain infinite property. We prove that two full essential extensions are approximately unitarily equivalent if and only if they induce the same element in $KL(A, M(B)/B).$ The set of approximately unitarily equivalence classes of full essential extensions forms a group. If $A$ satisfies the Universal Coefficient Theorem, it is can be identified with $KL(A, M(B)/B).$

Affiliated with

Also associated with

No associations

Rating

Full extensions and approximate unitary equivalences 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 Full extensions and approximate unitary equivalences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Full extensions and approximate unitary equivalences will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-569987