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Classifying Hilbert bundles. (English) Zbl 0275.46050


MSC:

46L05 General theory of \(C^*\)-algebras
55R65 Generalizations of fiber spaces and bundles in algebraic topology
55R15 Classification of fiber spaces or bundles in algebraic topology
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
Full Text: DOI

References:

[1] Arens, R.; Kaplansky, I., Topological representations of algebras, Trans. Amer. Math. Soc., 63, 457-481 (1948) · Zbl 0032.00702
[2] Brown, M., Locally flat imbeddings of topological manifolds, Ann. Math., Series 2, 75, 331-341 (1962) · Zbl 0201.56202
[3] Dixmier, J., Champs continus d’espaces hilbertiennes et de \(C^∗\)-algèbres (II), J. Math. Pures Appl., XLII (1963) · Zbl 0127.33301
[4] Dixmier, J., Les \(C^∗\)-Algèbres et leurs Representations (1969), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0174.18601
[5] Dixmier, J.; Douady, A., Champs continus d’espaces hilbertiennes, Bull. Soc. Math. France, 19, 227-283 (1963) · Zbl 0127.33102
[6] Dupré, M. J., The classification of Hilbert bundles, (Ph.D. Dissertation (August, 1972), University of Pennsylvania) · Zbl 0536.46048
[7] Fell, J. M.G, An extension of Mackey’s method to Banach \(^∗\)-algebraic bundles, Mem. A.M.S., 90 (1969) · Zbl 0194.44301
[8] Fell, J. M.G, The structure of algebras of operator fields, Acta Math., 106, 233-280 (1961) · Zbl 0101.09301
[9] Godement, R., Sur la théorie des représentations unitaires, Ann. Math., Series 2, 53, 68-124 (1951) · Zbl 0042.34606
[10] Godement, R., Théorie générale des sommes continus d’espaces de Banach, C. R. Acad. Sci. Paris, 228, 1321-1323 (1949) · Zbl 0033.37602
[11] Grothendieck, A., A General Theory of Fibre Spaces with Structure Sheaf (1955), University of Kansas
[12] Husemoller, D., Fibre Bundles (1966), McGraw-Hill: McGraw-Hill New York · Zbl 0144.44804
[13] Kaplansky, I., Normed algebras, Duke Math. J., 16, 399-418 (1949) · Zbl 0033.18701
[14] Kaplansky, I., The structure of certain operator algebras, Trans. Amer. Math. Soc., 70, 219-255 (1951) · Zbl 0042.34901
[15] Marechal, O., Champs mesurables d’espaces hilbertiennes, Bull. Sci. Math., XCIII, 113-143 (1969) · Zbl 0186.45601
[16] Steenrod, N., The Topology of Fibre Bundles (1951), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0054.07103
[17] Tomiyama, J., Topological representations of \(C^∗\)-algebras, Tohoku Math. J., Series 2, 14, 187-204 (1962) · Zbl 0216.16201
[18] Tomiyama, J.; Takesaki, M., Application of fibre bundles to the certain class of \(C^∗\)-algebras, Tohoku Math. J., Series 2, 13, 498-522 (1961) · Zbl 0113.09701
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