Pacific Journal of Mathematics
- Pacific J. Math.
- Volume 67, Number 1 (1976), 131-153.
The structure of standard $C^*$-algebras and their representations.
Full-text: Open access
Article information
Source
Pacific J. Math., Volume 67, Number 1 (1976), 131-153.
Dates
First available in Project Euclid: 8 December 2004
Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102817669
Mathematical Reviews number (MathSciNet)
MR0428049
Zentralblatt MATH identifier
0339.46040
Subjects
Primary: 46L05: General theory of $C^*$-algebras
Citation
Ching, Wai Mee. The structure of standard $C^*$-algebras and their representations. Pacific J. Math. 67 (1976), no. 1, 131--153. https://projecteuclid.org/euclid.pjm/1102817669
References
- [1] C. Akemann, A Gelfand representation theory for C*-algebras, Pacific J. Math., 39 (1971), 1-11.
- [2] S. Anastasio and P. Willig, Structure of Factors, Arithmetic Press, New York, 1974.
- [3] H. Behncke and W. Bos, A class of C*-algebras,Proc. Amer. Math. Soc, 40(1973), 128-134.Mathematical Reviews (MathSciNet): MR48:9407
- [4] H. Behncke, F. Krau/3 and H. Leptin, C*-algebrem mit geordneten Ideal Folgen, Functional Analysis, 1O (1972), 204-211.
- [5] S. Berberian, Baer *-rings, Springer-Verlag, Berlin-Heidelberg-New York, 1972.Mathematical Reviews (MathSciNet): MR55:2983
- [6] F. Bonsall and J. Duncan, Completed Normed Algebras, Springer-Verlag, Berlin- Heidelberg-New York, 1973.
- [7] N. Bourbaki, Topologie Generate, Chap. I, Hermann, Paris, 1958.Mathematical Reviews (MathSciNet): MR30:3439
- [8] J. Calkin, Two-sided idaals and congruences in the ring of bounded operators in Hilbert space, Ann. Math., 42 (1941), 839-873.
- [9] W. Ching, A continuumof non-isomorphic non-hyper finite factors, Comm. Pure Appl. Math., 23 (1970), 921-937.
- [10] J. Dauns, The primitive ideal space of a C*-algebra, Canad. J. Math., 26 (1974), 42-49.
- [11] J. Dauns and K. Hofmann, Representationsof rings by sections, Memoir Amer. Math. Soc, 83 (1968), 180.
- [12] J. Dixmier, Sur les C*-algebres,Bull. Soc. Math. France, 89 (1960), 95-112.Mathematical Reviews (MathSciNet): MR22:12408
- [13] J. Dixmier,Les C*-algebreset leurs representations, Gauthier-Villars, Paris, 1964.Mathematical Reviews (MathSciNet): MR30:1404
- [14] J. Dixmier and A. Douady, Champs continus d'espaces hilbertiens et de C*-algebres, Bull. Soc. Math. France, 91 (1963), 227-284.
- [15] G. Emch, Algebraic Methods in StatisticalMechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972.Zentralblatt MATH: 0235.46085
- [16] J. Fell, The dual spaces of C*-algebras, Trans. Amer. Math. Soc, 94 (1960), 365-405.
- [17] J. Fell,The structure of algebras of operator fields, Acta Math., 106 (1961), 233-280.
- [18] I. Gelfand and M. Naimark, On the imbedding of normed rings into the ring of operators in Hilbert space, Mat. Sb., 12 (1943), 197-213.
- [19] J. Glimm, A Stone-Weierstrass theorem forC*-algebras, Ann. Math., 72 (1960), 216-244.
- [20] R. Godement, Sur la theorie des representations unitaires, Ann. Math., 53 (1951), 68-124.
- [21] H. Halpern, Irreducible module homomorphisms of a von Neumannalgebra into its center, Trans. Amer. Math. Soc, 140 (1969), 195-221.
- [22] N. Jacobson, Structureof rings, Amer. Math. Soc Colloq. Publ. no. 37, Providence, 1956.
- [23] I. Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc, 7O (1950), 219-255.
- [24] I. Kaplansky, Projections in Banach algebras, Ann. Math., 53 (1951), 235-249.
- [25] E. Lance, Notes on the Glimm-SakaiTheorem, University of Newcastle upon Tyne, 1971.
- [26] D. McDuff, Uncountably many W-factors, Ann. Math., 90 (1969), 372-377.
- [27] J. von Neumann, On rings of operators'. Reduction theory, Ann. Math., 50(1949), 401-485.
- [28] R. Powers, Representations of uniformlyhyperfinite algebras and their associated von Neumann rings, Ann. Math., 8 (1967), 138-171.
- [29] C. Rickart, General Theory of Banach Algebras, van Nostand, Princeton, 1960.
- [30] S. Sakai, C*-Algebras and W*-Algebras, Springer-Verlag,Berlin-Heidelberg-New York, 1971.Mathematical Reviews (MathSciNet): MR56:1082
- [31] H. Takemoto, On a characterizationof AW*-modulesand a representation of Gelfand type of non-commutativeoperator algebras, Michigan J. Math., 20 (1973), 115-127.
Pacific Journal of Mathematics, A Non-profit Corporation

- You have access to this content.
- You have partial access to this content.
- You do not have access to this content.
More like this
- Reduced contragredient Lie algebras and PC Lie algebras
Sasano, Nagatoshi, Osaka Journal of Mathematics, 2019 - The Cuntz Comparison in the Standard
C
*
-Algebra
Fang, Xiaochun, Sze, Nung-Sing, and Xu, Xiao-Ming, Abstract and Applied Analysis, 2014 - Contragredient Lie algebras and Lie algebras associated with a standard pentad
Sasano, Nagatoshi, Tsukuba Journal of Mathematics, 2018
- Reduced contragredient Lie algebras and PC Lie algebras
Sasano, Nagatoshi, Osaka Journal of Mathematics, 2019 - The Cuntz Comparison in the Standard
C
*
-Algebra
Fang, Xiaochun, Sze, Nung-Sing, and Xu, Xiao-Ming, Abstract and Applied Analysis, 2014 - Contragredient Lie algebras and Lie algebras associated with a standard pentad
Sasano, Nagatoshi, Tsukuba Journal of Mathematics, 2018 - Subfactors, Planar Algebras, and Rotations
Burns, Michael, , 2017 - Analysis Over $C^*$-Algebras and the Oscillatory Representation
Krýsl, Svatopluk, Journal of Geometry and Symmetry in Physics, 2014 - Analysis Over $C^*$-Algebras and the Oscillatory Representation
Krýsl, Svatopluk, , 2014 - Dressing orbits and a quantum Heisenberg group algebra
Kahng, Byung-Jay, Illinois Journal of Mathematics, 2004 - Principal ideals in subalgebras of groupoid $C^*$-algebras
Krishnan, Srilal, Illinois Journal of Mathematics, 2002 - Homotopy algebra structures on twisted tensor products and string topology operations
Miller, Micah, Algebraic & Geometric Topology, 2011 - Cluster algebras and quantum affine algebras
Hernandez, David and Leclerc, Bernard, Duke Mathematical Journal, 2010