Ghostly ideals in uniform Roe algebras

Jiawen Zhang  (Fudan University)

14:00-15:00,July 31,2023   文附楼 (Wenfu Building) 219

Abstract:

Inspired by the ideal of ghost operators coming from expander graphs, we introduce a notion of ghostly ideal in a uniform Roe algebra, whose elements are locally invisible in certain directions at infinity. We show that the geometric ideal and the ghostly ideal are respectively the smallest and the largest element in the lattice of ideals with a common invariant open subset. Moreover, we introduce a notion of partial Property A for a metric space to characterise the situation in which the geometric ideal coincides with the ghostly ideal. This is a joint work with Qin Wang.

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