TY - JOUR
T1 - Ideal spaces of the Haagerup tensor product of C*-algebras
AU - Archbold, Robert J.
AU - Somerset, Douglas W.B.
AU - Kaniuth, Eberhard
AU - Schlichting, Günter
PY - 1997/2
Y1 - 1997/2
N2 - Following the work of Allen, Sinclair and Smith on the primitive ideal space of the Haagerup tensor product A ⊗h, B of C*-algebras A and B, we investigate the hull-kernel topology and use this to determine various other ideal spaces and their topologies in relation to the corresponding ideal spaces of A and B. We study the semi-continuity of norm functions I → ∥cursive Greek chi + I∥ (cursive Greek chi ∈ A ⊗h B) on these ideal spaces and identify the separated points of Prim(A ⊗h B). Finally, we exhibit several conditions each of which is equivalent to the quasi-standardness of A ⊗h B.
AB - Following the work of Allen, Sinclair and Smith on the primitive ideal space of the Haagerup tensor product A ⊗h, B of C*-algebras A and B, we investigate the hull-kernel topology and use this to determine various other ideal spaces and their topologies in relation to the corresponding ideal spaces of A and B. We study the semi-continuity of norm functions I → ∥cursive Greek chi + I∥ (cursive Greek chi ∈ A ⊗h B) on these ideal spaces and identify the separated points of Prim(A ⊗h B). Finally, we exhibit several conditions each of which is equivalent to the quasi-standardness of A ⊗h B.
UR - http://www.scopus.com/inward/record.url?scp=0031069001&partnerID=8YFLogxK
U2 - 10.1142/S0129167X97000020
DO - 10.1142/S0129167X97000020
M3 - Article
AN - SCOPUS:0031069001
SN - 0129-167X
VL - 8
SP - 1
EP - 29
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 1
ER -