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Search: MSC category 47C15 ( Operators in $C^$- or von Neumann algebras *$- or von Neumann algebras * )

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1. CMB 1998 (vol 41 pp. 240)

Xia, Jingbo
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

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