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

Ved Prakash Gupta, Ranjana Jain and Bharat Talwar

Mathematische Nachrichten, 2020, vol. 293, issue 1, 101-114

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.

Date: 2020
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https://doi.org/10.1002/mana.201800496

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