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Morita equivalence for C\(^*\)-algebras and W\(^*\)-algebras.(English)Zbl 0295.46099


MSC:

46M15 Categories, functors in functional analysis
46L05 General theory of \(C^*\)-algebras
46L10 General theory of von Neumann algebras
46M05 Tensor products in functional analysis
18D99 Categorical structures
18B99 Special categories

Cite

References:

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[4]Bourbaki, N., Topologie Générale, (Actualités Sci. Indust., 1045 (1958), Hermann: Hermann Paris), ch. 9 ·Zbl 0085.37103
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[12]Ernest, J., A new group algebra for locally compact groups, Am. J. Math., 86, 467-492 (1964) ·Zbl 0211.15402
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[14]Ernest, J., Hopf-von-Neumann algebras, (Proc. Functional Analysis Conf. (1967), Thompson: Thompson Washington, D.C), 192-215, Irvine ·Zbl 0219.43004
[15]J. Ernest, The enveloping algebra of a covariant system, Commun. Math. Phys., to appear.; J. Ernest, The enveloping algebra of a covariant system, Commun. Math. Phys., to appear. ·Zbl 0188.44702
[16]J. Ernest, A duality theorem for the automorphism group of a covariant system, Commun. Math. Phys., to appear.; J. Ernest, A duality theorem for the automorphism group of a covariant system, Commun. Math. Phys., to appear. ·Zbl 0188.44703
[17]Freyd, P., Abelian Categories (1964), Harper and Row: Harper and Row New York ·Zbl 0121.02103
[18]Gardner, L. T., On the “third definition” of the topology on the spectrum of a \(C^∗\)-algebra, Can. J. Math., 23, 445-450 (1971) ·Zbl 0217.16803
[19]Guichardet, A., Sur la catégorie des algèbres de von Neumann, Bull. Sci. Math., 90, 41-64 (1966) ·Zbl 0154.39001
[20]Hewitt, E.; Ross, K. A., The Tannaka-Krein duality theorems, Jber. Deutsch. Math.-Verein, 71, 61-83 (1969) ·Zbl 0221.22007
[21]Kaplansky, I., Modules over operator algebras, Trans. Am. Math. Soc., 75, 839-858 (1953) ·Zbl 0051.09101
[22]Kac, G. I., Ring-groups and the principle of duality I, Tr. Moskov. Mat. Obšč., 12, 259-300 (1963)
[23]Mackey, G. W., Induced representations of locally compact groups I, Ann. Math., 55, 101-139 (1952) ·Zbl 0046.11601
[24]Mackey, G. W., Unitary representations of group extensions I, Acta Math., 99, 265-311 (1958) ·Zbl 0082.11301
[25]MacLane, S., Categories for the Working Mathematician (1971), Springer: Springer Berlin ·Zbl 0232.18001
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[27]Paschke, W. L., Inner product modules over \(B^∗\)-algebras, Trans. Am. Math. Soc., 182, 443-468 (1973) ·Zbl 0239.46062
[28]Rieffel, M. A., Multipliers and tensor products of\(L^P\)-spaces of locally compact groups, Studia Math., 33, 71-82 (1969) ·Zbl 0177.41702
[29]Rieffel, M. A., Unitary representations induced from compact subgroups, Studia Math., 42, 145-175 (1972) ·Zbl 0213.03904
[30]Rieffel, M. A., Induced representations of \(C^∗\)-algebras, Advan. Math., 13, 176-257 (1974) ·Zbl 0284.46040
[31]Rivano, N. Saavedra, Catégories tannakiennes, Bull. Soc. Math. France, 100, 417-430 (1972) ·Zbl 0246.14003
[32]Sakai, S., \(C^∗\)-algebras and \(W^∗\)-algebras (1971), Springer: Springer Berlin ·Zbl 0219.46042
[33]Takesaki, M., A duality in the representation theory of \(C^∗\)-algebras, Ann. Math., 85, 370-382 (1967) ·Zbl 0149.34502
[34]Takesaki, M., A characterization of group algebras as a converse of Tannaka-Stinespring-Tatsuuma duality theorem, Am. J. Math., 91, 529-564 (1969) ·Zbl 0182.18103
[35]Takesaki, M., Tomita’s theory of modular Hilbert algebras and its applications, (Lecture Notes in Math., 128 (1970), Springer: Springer Berlin) ·Zbl 0193.42502
[36]Tannaka, T., Über den dualität der nicht-kommutativen topologischen Gruppen, Tohoku Math. J., 45, 1-12 (1938) ·JFM 64.0362.01
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[38]Watts, C., Intrinsic characterization of some additive functors, Proc. Am. Math. Soc., 11, 5-8 (1960) ·Zbl 0093.04101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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