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On closed Lie ideals of certain tensor products of C∗‐algebras II

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  • Ved Prakash Gupta
  • Ranjana Jain
  • Bharat Talwar

Abstract

We identify all closed Lie ideals of A⊗αB and B(H)⊗αB(H), where ⊗α is either the Haagerup tensor product, the Banach space projective tensor product or the operator space projective tensor product, A is any simple C∗‐algebra, B is any C∗‐algebra with one of them admitting no tracial states, and H is an infinite dimensional separable Hilbert space. Further, generalizing a result of Marcoux, we also identify all closed Lie ideals of A⊗minB, where A is a simple C∗‐algebra with at most one tracial state and B is any commutative C∗‐algebra.

Suggested Citation

  • Ved Prakash Gupta & Ranjana Jain & Bharat Talwar, 2020. "On closed Lie ideals of certain tensor products of C∗‐algebras II," Mathematische Nachrichten, Wiley Blackwell, vol. 293(1), pages 101-114, January.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:1:p:101-114
    DOI: 10.1002/mana.201800496
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