论文标题
$ M_D $ - Approximation属性和Unitarisability
The $M_d$-Approximation Property and Unitarisability
论文作者
论文摘要
我们通过Pisier引入的HERZ-SCHUR乘数$ m_d（g）$（$ d \ geq 2 $）来定义Haagerup-Kraus近似属性的加强。我们表明，满足所有$ d \ geq 2 $的可满足此属性的一单位群体都是可正常的。此外，我们表明，在有限维猫（0）Cube ComplexS上正确作用的组满足了所有$ d \ geq 2 $的$ m_d $ -ap。我们还举例说明所有$ d \ geq 2 $满足$ m_d $ -ap的非智能amenable群组的示例。
We define a strengthening of the Haagerup-Kraus approximation property by means of the subalgebras of Herz-Schur multipliers $M_d(G)$ ($d\geq 2$) introduced by Pisier. We show that unitarisable groups satisfying this property for all $d\geq 2$ are amenable. Moreover, we show that groups acting properly on finite-dimensional CAT(0) cube complexes satisfy $M_d$-AP for all $d\geq 2$. We also give examples of non-weakly amenable groups satisfying $M_d$-AP for all $d\geq 2$.
