P-Tensor Product for Group C *-Algebras

Yufang Li and Zhe Dong
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Yufang Li: Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
Zhe Dong: Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

Mathematics, 2020, vol. 8, issue 4, 1-14

Abstract: 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 ≤ + ∞ .

Keywords: p-tensor product; amenability; Haagerup property; Primary20F65 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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