Author:
TALWAR BHARAT,JAIN RANJANA
Abstract
AbstractFor a locally compact Hausdorff space X and a C*-algebra A with only finitely many closed ideals, we discuss a characterization of closed ideals of C0(X,A) in terms of closed ideals of A and a class of closed subspaces of X. We further use this result to prove that a closed ideal of C0(X)⊗minA is a finite sum of product ideals. We also establish that for a unital C*-algebra A, C0(X,A) has the centre-quotient property if and only if A has the centre-quotient property. As an application, we characterize the closed Lie ideals of C0(X,A) and identify all the closed Lie ideals of HC0(X)⊗minB(H), H being a separable Hilbert space.
Publisher
Cambridge University Press (CUP)
Reference17 articles.
1. Lie ideals: from pure algebra to C*-algebras;Brešar;J. Reine Angew. Math,2008
2. On Banach space projective tensor product of $$C^*$$-algebras
3. The ideal structure of the Haagerup tensor product of C*-algebras;Allen;J. Reine Angew. Math,1993
4. [13] Naimark, M. A. , Normed algebras (Groningen, 1964).
5. IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS
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