Geodesic
CLOSED IDEALS AND LIE IDEALS OF MINIMAL TENSOR PRODUCT OF CERTAIN C*-ALGEBRAS
Glasgow mathematical journal, Tome 63 (2021) no. 2, pp. 414-425

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DOI

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)⊗min A 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. 
TALWAR, BHARAT; JAIN, RANJANA. CLOSED IDEALS AND LIE IDEALS OF MINIMAL TENSOR PRODUCT OF CERTAIN C*-ALGEBRAS. Glasgow mathematical journal, Tome 63 (2021) no. 2, pp. 414-425. doi: 10.1017/S0017089520000270
@article{10_1017_S0017089520000270,
     author = {TALWAR, BHARAT and JAIN, RANJANA},
     title = {CLOSED {IDEALS} {AND} {LIE} {IDEALS} {OF} {MINIMAL} {TENSOR} {PRODUCT} {OF} {CERTAIN} {C*-ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {414--425},
     year = {2021},
     volume = {63},
     number = {2},
     doi = {10.1017/S0017089520000270},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000270/}
}
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