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\(W^*\)-algebras and nonabelian harmonic analysis. (English) Zbl 0242.22010

MSC:
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22D35 Duality theorems for locally compact groups
22D10 Unitary representations of locally compact groups
43A10 Measure algebras on groups, semigroups, etc.
43A35 Positive definite functions on groups, semigroups, etc.
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[1] Dixmier, J., LES algèbres d’opérateurs dans l’espace hilbertien, (1969), Gauthier-Villars Paris · Zbl 0175.43801
[2] Dixmier, J., LES C∗-algèbres et leurs représentations, (1965), Gauthier-Villars Paris · Zbl 0152.32902
[3] Dunford, N.; Schwartz, J.T., ()
[4] Ernest, J., A new group algebra for locally compact groups. I, Amer. J. math., 86, 467-492, (1964) · Zbl 0211.15402
[5] Ernest, J., A new group algebra for locally compact groups. II, Canad. J. math., 17, 604-615, (1965) · Zbl 0211.15403
[6] Ernest, J., Hopf-von Neumann algebras, () · Zbl 0219.43004
[7] Eymard, P., L’algèbre de Fourier d’un groupe localement compact, Bull. soc. math. France, 92, 181-236, (1964) · Zbl 0169.46403
[8] Kadison, R.V., Isometries of operator algebras, Ann. of math., 54, 325-338, (1951) · Zbl 0045.06201
[9] Kelley, J.L.; Namioka, I., Linear topological spaces, (1953), Van Nostrand New York
[10] Loomis, L.H., An introduction to abstract harmonic analysis, (1953), Van Nostrand New York · Zbl 0165.15502
[11] Misonou, Y., On the direct product of W∗-algebras, Tôhoku math. J., 6, 189-204, (1954) · Zbl 0057.34201
[12] Naimark, M.A., Normed rings, (1964), Noordhoff Groningen, Netherlands · Zbl 0137.31703
[13] Pontrjagin, L., Topological groups, (1939), Princeton University Press Princeton, NJ, (translated by Emma Lehmer) · JFM 65.0872.02
[14] Rickart, C.E., General theory of Banach algebras, (1960), Van Nostrand New York · Zbl 0084.33502
[15] Rudin, W., Fourier analysis on groups, (1962), Interscience New York · Zbl 0107.09603
[16] Saito, K., On a duality for locally compact groups, Tôhoku math. J., 20, 355-367, (1968) · Zbl 0185.39102
[17] Sakai, S., The theory of W∗-algebras, notes, (1962), Dept. of Math., Yale University New Haven, CT
[18] Segal, I.E., Equivalences of measure spaces, Amer. J. math., 73, 275-313, (1952) · Zbl 0042.35502
[19] Stinespring, W.F., Integration theorems for gages and duality for unimodular groups, Trans. amer. math. soc., 90, 15-56, (1959) · Zbl 0085.10202
[20] Stormer, E., On the Jordan structure of C∗-algebras, Trans. amer. math. soc., 120, 438-447, (1965) · Zbl 0136.11401
[21] Suzuki, M., Structure of a group and the structure of its lattice of subgroups, (1956), Springer-Verlag Berlin · Zbl 0070.25406
[22] Takesaki, M., On the conjugate space of operator algebra, Tôhoku math. J., 10, 194-203, (1958) · Zbl 0089.10703
[23] Takesaki, M., A characterization of group algebras as a converse of tannaka-Stinespring-tatsuuma duality theorem, Amer. J. math., 91, 529-564, (1969) · Zbl 0182.18103
[24] Takesaki, M., Tomita’s theory of modular hubert algebras and its applications, (1970), Springer-Verlag Berlin · Zbl 0193.42502
[25] Tannaka, T., Über den dualität der nicht-kommutatinen topologischen gruppen, Tôhoku math. J., 45, 1-12, (1938) · JFM 64.0362.01
[26] Tatsuuma, N., A duality theorem for locally compact groups, J. math. Kyoto univ., 6, 187-293, (1967) · Zbl 0184.17402
[27] Walter, M.E., Group duality and isomorphisms of Fourier and Fourier-Stieltjes algebras from a W∗-algebra point of view, Bull. amer. math. soc., 76, 1321-1325, (1970) · Zbl 0204.14801
[28] Wendel, J.G., Left centralizers and isomorphisms of group algebras, Pacific J. math., 2, 251-261, (1952) · Zbl 0049.35702
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