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P-Tensor Product for Group C*-Algebras

by Yufang Li 1,2,* and Zhe Dong 1
1
Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
2
Department of Mathematical and Statistics, Guizhou University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 627; https://doi.org/10.3390/math8040627
Received: 25 March 2020 / Revised: 10 April 2020 / Accepted: 14 April 2020 / Published: 18 April 2020
In this paper, we introduce new tensor products p ( 1 p + ) on C p * ( Γ ) C p * ( Γ ) and c 0 on C c 0 * ( Γ ) C c 0 * ( Γ ) for any discrete group Γ . We obtain that for 1 p < + C p * ( Γ ) m a x C p * ( Γ ) = C p * ( Γ ) p C p * ( Γ ) if and only if Γ is amenable; C c 0 * ( Γ ) m a x C c 0 * ( Γ ) = C c 0 * ( Γ ) c 0 C c 0 * ( Γ ) if and only if Γ has Haagerup property. In particular, for the free group with two generators F 2 we show that C p * ( F 2 ) p C p * ( F 2 ) C q * ( F 2 ) q C q * ( F 2 ) for 2 q < p + . View Full-Text
Keywords: p-tensor product; amenability; Haagerup property; 2000 MR Subject Classification; Primary20F65 p-tensor product; amenability; Haagerup property; 2000 MR Subject Classification; Primary20F65
MDPI and ACS Style

Li, Y.; Dong, Z. P-Tensor Product for Group C*-Algebras. Mathematics 2020, 8, 627.

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