On closed Lie ideals of certain tensor products of C∗‐algebras II. Issue 1 (22nd November 2019)

• Record Type: Journal Article
• Authors: Gupta, Ved Prakash; Jain, Ranjana; Talwar, Bharat
• Is Part Of: Mathematische Nachrichten. Volume 293:Issue 1(2020)
• Page Start: 101
• Page End: 114
• Publication Date: 2019-11-22
• Subjects: Banach algebras -- C∗‐algebras -- commutators -- ideals -- Lie ideals -- operator spaces -- tensor products -- 46L06 -- 46L07; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201800496
• Languages: English
• ISSNs: 0025-584X

Abstract

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.