Search: MSC category 47C15 ( Operators in $C^$- or von Neumann algebras *$- or von Neumann algebras * )  Expand all Collapse all Results 1 - 2 of 2 1. CMB 2016 (vol 59 pp. 326) Jiang, Chunlan; Shi, Rui  On the Uniqueness of Jordan Canonical Form Decompositions of Operators by$K$-theoretical Data In this paper, we develop a generalized Jordan canonical form theorem for a certain class of operators in$\mathcal {L}(\mathcal {H})$. A complete criterion for similarity for this class of operators in terms of$K$-theory for Banach algebras is given. Keywords:strongly irreducible operator, similarity invariant, reduction theory of von Neumann algebras,$K$-theoryCategories:47A15, 47C15, 47A65 2. CMB 1998 (vol 41 pp. 240) Xia, Jingbo  On certain$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