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On tensor products of certain group \(C^*\)-algebras. (English) Zbl 0358.46040


MSC:

46L05 General theory of \(C^*\)-algebras
46L10 General theory of von Neumann algebras
46M05 Tensor products in functional analysis
22D15 Group algebras of locally compact groups
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
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References:

[1] Dixmier, J., Les \(C^∗\)-algèbres et leurs représentations (1969), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0174.18601
[2] Dixmier, J., Les algèbres d’opérateurs dans l’espace Hilbertien (1969), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0175.43801
[3] E. G. Effros and E. C. Lance; E. G. Effros and E. C. Lance · Zbl 0372.46064
[4] Guichardet, A., Tensor products of \(C^∗\)-algebras, Soviet Math. Dokl., 6, 210-213 (1965) · Zbl 0127.07303
[5] Hall, M., The theory of groups (1959), Macmillan: Macmillan New York · Zbl 0084.02202
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[7] E. C. Lance; E. C. Lance
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[9] Sakai, S., The theory of \(W^∗\)-algebras, (lecture notes (1962), Yale University) · Zbl 0267.46048
[10] Sakai, S., \(C^∗\)-algebras and \(W^∗\)-algebras (1971), Springer-Verlag: Springer-Verlag Berlin · Zbl 0219.46042
[11] Takesaki, M., On the cross-norm of the direct product of \(C^∗\)-algebras, Tôhoku Math. J., 16, 111-122 (1964) · Zbl 0127.07302
[12] Tomiyama, J., Applications of Fubini type theorem to the tensor product of \(C^∗\)-algebras, Tôhoku Math. J., 19, 213-226 (1967) · Zbl 0166.11401
[13] Tomiyama, J., Tensor products and projections of norm one in von Neumann algebras, (seminar notes Mathematical Institute (1971), Univ. Copenhagen) · Zbl 0176.44002
[14] Wassermann, S., Extension of normal functionals on \(W^∗\)-tensor products, (Math. Proc. Cambridge Phil. Soc., 78 (1975)), 301-307 · Zbl 0315.46057
[15] Wassermann, S., The slice map problem for \(C^∗\)-algebras, (Proc. London Math. Soc., 32 (1976)), 537-559, (3) · Zbl 0321.46048
[16] Wulfsohn, A., The primitive spectrum of a tensor product of \(C^∗\)-algebras, (Proc. Amer. Math. Soc., 19 (1968)), 1094-1096 · Zbl 0174.18603
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