6 papers · 1 filter
Characterisations for coarse embeddability via quasi-locality and Schur multipliers
Kang Li, Jiawen Zhang, Jingming Zhu
We establish three new characterisations of coarse embeddability into Hilbert space for discrete metric spaces of bounded geometry in terms of escaping quasi-local couplings, Schur…
Quantitative decomposition and approximation for quasi-local operators
Jiawen Zhang, Jingming Zhu
We develop a quantitative approach to quasi-local operators with bounded block-rank. Our main results are a quantitative decomposition for quasi-local operators into block-rank-one…
-Theoretic Comparison of Roe and Quasi-Local Algebras via Projections
Kang Li, Jiawen Zhang, Jingming Zhu
A central question in higher index theory and operator algebras is whether the Roe algebra and the quasi-local algebra associated with a metric space of bounded geometry coincide,…
Transfinite Extension of Nuclear Dimension
Jingming Zhu, Jiawen Zhang
In this paper, we introduce a notion of transfinite nuclear dimension for -algebras, which coincides with the nuclear dimension when taking values in natural numbers. We use i…
Two versions of the uniform Roe algebras for spaces without bounded geometry
Vladimir Manuilov, Jingming Zhu
We consider two versions of the uniform Roe algebra for uniformly discrete spaces without bounded geometry and discuss some of their properties.
Extensions of Hilbert C*-modules: classification in simple cases
Vladimir Manuilov, Jingming Zhu
Theory of extensions of Hilbert C*-modules was developed by D. Bakic and B. Guljas. An easy observation shows that in the case, when the underlying C*-algebra extension is commutat…