A decomposition theory for unitary representations of locally compact groups

A decomposition theory for unitary representations of locally compact groups
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Trans. Amer. Math. Soc. 104 (1962), 252-277

DOI: https://doi.org/10.1090/S0002-9947-1962-0139959-X

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References

Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722

Sur les structures Boréliennes du spectre d’une

algèbre

6

J. Dixmier, Dual et quasi-dual d’une algèbre de Banach involutive, Trans. Amer. Math. Soc. 104 (1962), 278–283 (French). MR 139960, DOI 10.1090/S0002-9947-1962-0139960-6
John Ernest, A decomposition theory for unitary representations of locally compact groups, Bull. Amer. Math. Soc. 67 (1961), 385–388. MR 130930, DOI 10.1090/S0002-9904-1961-10629-0
J. M. G. Fell, The dual spaces of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 94 (1960), 365–403. MR 146681, DOI 10.1090/S0002-9947-1960-0146681-0
J. M. G. Fell, $C^{\ast }$-algebras with smooth dual, Illinois J. Math. 4 (1960), 221–230. MR 124754
James Glimm, Type I $C^{\ast }$-algebras, Ann. of Math. (2) 73 (1961), 572–612. MR 124756, DOI 10.2307/1970319
Alain Guichardet, Sur un problème posé par G. W. Mackey, C. R. Acad. Sci. Paris 250 (1960), 962–963 (French). MR 110027
Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. MR 1653399

Topologie

Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0054173

The theory of group representations

George W. Mackey, On induced representations of groups, Amer. J. Math. 73 (1951), 576–592. MR 42420, DOI 10.2307/2372309
George W. Mackey, Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193–221. MR 56611, DOI 10.2307/1969786
George W. Mackey, Borel structure in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134–165. MR 89999, DOI 10.1090/S0002-9947-1957-0089999-2
George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265–311. MR 98328, DOI 10.1007/BF02392428
F. I. Mautner, Unitary representations of locally compact groups. I, Ann. of Math. (2) 51 (1950), 1–25. MR 32650, DOI 10.2307/1969494
M. A. Naĭmark, Factor-representations of a locally compact group, Soviet Math. Dokl. 1 (1960), 1064–1066. MR 0124752
John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, DOI 10.2307/1969463
I. E. Segal, Decompositions of operator algebras. I, Mem. Amer. Math. Soc. 9 (1951), 67. MR 44749