IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p627-d347270.html
   My bibliography  Save this article

P-Tensor Product for Group C *-Algebras

Author

Listed:
  • Yufang Li

    (Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
    Department of Mathematical and Statistics, Guizhou University, Guiyang 550025, China)

  • Zhe Dong

    (Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China)

Abstract

In this paper, we introduce new tensor products ⊗ p ( 1 ≤ p ≤ + ∞ ) on C ℓ p * ( Γ ) ⊗ C ℓ 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 ℓ p * ( Γ ) ⊗ m a x C ℓ p * ( Γ ) = C ℓ p * ( Γ ) ⊗ p C ℓ 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 ℓ p * ( F 2 ) ⊗ p C ℓ p * ( F 2 ) ≇ C ℓ q * ( F 2 ) ⊗ q C ℓ q * ( F 2 ) for 2 ≤ q < p ≤ + ∞ .

Suggested Citation

  • Yufang Li & Zhe Dong, 2020. "P-Tensor Product for Group C *-Algebras," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:627-:d:347270
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/627/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/627/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    p-tensor product; amenability; Haagerup property; ; Primary20F65;
    All these keywords.

    JEL classification:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:627-:d:347270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.