𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Almost Commuting Unitaries and Classification of Purely Infinite SimpleC*-Algebras

✍ Scribed by Huaxin Lin


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
282 KB
Volume
155
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis


We show that, for any irrational rotational algebra A % , A % O 2 $O 2 . This is proved by combining recently established results for C*-algebras of real rank zero with the following result:

For any =>0, there is $>0, such that for any pair of unitaries u, v in any purely infinite simple C*-algebra A with K 1 (A)=0 satisfies &uv&vu&<$ and }(u, v)=0.

There is a pair of commuting unitaries U, V # A with finite spectrum such that &u&U&<= and &v&V&<=.

More general results concerning almost commuting unitaries are also obtained.