1. CMB 1998 (vol 41 pp. 240)
|On certain $K$-groups associated with minimal flows |
It is known that the Toeplitz algebra associated with any flow which is both minimal and uniquely ergodic always has a trivial $K_1$-group. We show in this note that if the unique ergodicity is dropped, then such $K_1$-group can be non-trivial. Therefore, in the general setting of minimal flows, even the $K$-theoretical index is not sufficient for the classification of Toeplitz operators which are invertible modulo the commutator ideal.
Categories:46L80, 47B35, 47C15