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Banach bundles of continuous functions and an integral representation theorem. (English) Zbl 0489.46051


MSC:

46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46H15 Representations of topological algebras
22D30 Induced representations for locally compact groups
55R65 Generalizations of fiber spaces and bundles in algebraic topology
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
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References:

[1] Sterling K. Berberian, Measure and integration, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1965. · Zbl 1210.28001
[2] N. Bourbaki, Intégration. III: Eléments de mathématique, Hermann, Paris, 1959.
[3] Charles W. Burden, The Hahn-Banach theorem in a category of sheaves, J. Pure Appl. Algebra 17 (1980), no. 1, 25 – 34. · Zbl 0438.46051
[4] J. M. G. Fell, An extension of Mackey’s method to Banach * algebraic bundles, Memoirs of the American Mathematical Society, No. 90, American Mathematical Society, Providence, R.I., 1969. · Zbl 0194.44301
[5] -, Induced representations and Banach \( ^{\ast}\)-algebraic bundles, Lecture Notes in Math., vol. 582, Springer-Verlag, Berlin and New York, 1977.
[6] Jean Renault, A groupoid approach to \?*-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. · Zbl 0433.46049
[7] A. K. Seda, Haar measures for groupoids, Proc. Roy. Irish Acad. Sect. A 76 (1976), no. 5, 25 – 36. · Zbl 0329.43002
[8] Anthony Karel Seda, Quelques résultats dans la catégorie des groupoïdes d’opérateurs, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 1, A21 – A24 (French, with English summary). · Zbl 0411.43001
[9] Joel J. Westman, Harmonic analysis on groupoids, Pacific J. Math. 27 (1968), 621 – 632. · Zbl 0167.44003
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