For 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.

中文翻译：

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某些 C*-代数的最小张量积的闭理想和李理想

对于局部紧致 Hausdorff 空间X和一个C*-代数一种只有有限多个封闭理想，我们讨论封闭理想的表征C0(X,A) 就封闭理想而言一种和一类封闭子空间X. 我们进一步用这个结果来证明一个封闭理想C0(X)⊗分钟一种是产品理想的有限和。我们还确定对于一个单位C*-代数一种,C0(X,A) 具有中心商性质当且仅当一种具有中心商性质。作为一个应用程序，我们描述了闭李理想C0(X,A) 并识别出所有封闭的李理想HC0(X)⊗分钟乙(H),H是一个可分离的希尔伯特空间。