C~*-代数的迹迹秩

引入C~*-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C~*-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR(I)≤k且TTR(A/I)=0,则TTR(A)≤k.     

Quasidiagonal representations of nilpotent groups

We show that every unitary representation of a discrete solvable virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G   approximately decomposes as a direct sum of finite dimensional approximate representations. In operator algebraic terms we show that C^?(G)$C^{?}(G)$ is strongly quasidiagonal.     

Multirectangular invariants for power Köthe spaces

Using some new linear topological invariants, isomorphisms and quasidiagonal isomorphisms are investigated on the class of first type power Köthe spaces [Proceedings of 7th Winter School in Drogobych, 1976, pp. 101-126; Turkish J. Math. 20 (1996) 237-289; Linear Topol. Spaces Complex Anal. 2 (1995) 35-44]. This is the smallest class of Köthe spaces containing all Cartesian and projective tensor products of power series spaces and closed with respect to taking of basic subspaces (closed linear hulls of subsets of the canonical basis). As an application, it is shown that isomorphic spaces from this class have, up to quasidiagonal isomorphisms, the same basic subspaces of finite (infinite) type.     

拟对角扩张Cuntz半群的某些性质

设O→J→A→B→O是一个拟对角扩张.作者证明如果J和B具有Cuntz半群的某些性质,则A也具有相同的半群性质.