On closed Lie ideals of certain tensor products of C∗‐algebras II. Issue 1 (22nd November 2019) - Gupta, Ved Prakash; Jain, Ranjana; Talwar, Bharat
Abstract: We identify all closed Lie ideals of A ⊗ α B and B ( H ) ⊗ α B ( 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 ⊗ min B, where A is a simple C ∗ ‐algebra with at most one tracial state and B is any commutative C ∗ ‐algebra.