Bounded rank of C*algebras
Abstract
We introduce a concept of the bounded rank (with respect to a positive constant) for unital C*algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given $n$ and $K > 0$ there exists a separable unital C*algebra $Z_{n}^{K}$ such that every other separable unital C*algebra of bounded rank with respect to $K$ at most $n$ is a quotient of $Z_{n}^{K}$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109100
 Bibcode:
 2001math......9100C
 Keywords:

 Operator Algebras;
 46L05
 EPrint:
 20 pages