Property <i>T</i> and strong property <i>T</i> for unital *-homomorphisms

doi:10.1007/s11464-020-0831-3

Front. Math. China

2020, Vol. 15

Issue (2) : 385-398 https://doi.org/10.1007/s11464-020-0831-3

RESEARCH ARTICLE

Property T and strong property T for unital *-homomorphisms

Qing MENG(

)

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

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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 nite if and only if G is amenable and the inclusion map i : $C r * (G) → β (l 2 (G))$ 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.

Keywords Unital *-homomorphism, unital C^*-algebra, *-bimodule, property T strong property T

Corresponding Author(s): Qing MENG

Issue Date: 18 May 2020

Cite this article:

Qing MENG. Property T and strong property T for unital *-homomorphisms[J]. Front. Math. China, 2020, 15(2): 385-398.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0831-3
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I2/385

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