Abstract
We introduce and study property T and strong property T for unital *-homomorphisms between two unital C*-algebras. We also consider the relations between property T and invariant subspaces for some canonical unital *-representations. As a corollary, we show that when G is a discrete group, G is finite if and only if G is amenable and the inclusion map \(i:C^*_r(G)\rightarrow\mathscr{B}(\ell^2(G))\) has property T. We also give some new equivalent forms of property T for countable discrete groups and strong property T for unital C*-algebras.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871303, 11701327), the China Postdoctoral Science Foundation (No. 2018M642633), the Natural Science Foundation of Shandong Province (No. ZR2019MA039), and the Shandong Province Higher Educational Science and Technology Program (No. J18KA238).
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Meng, Q. Property T and strong property T for unital *-homomorphisms. Front. Math. China 15, 385–398 (2020). https://doi.org/10.1007/s11464-020-0831-3
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DOI: https://doi.org/10.1007/s11464-020-0831-3