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Equivalence and traces on \(C^*\)-algebras. (English) Zbl 0427.46042


MSC:

46L05 General theory of \(C^*\)-algebras
46L35 Classifications of \(C^*\)-algebras
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[1] Behncke, H.; Krauss, F.; Leptin, H., \(C^∗\)-Algebren mit geordneten Ideal Folgen, J. Functional Analysis, 10, 204-211 (1972) · Zbl 0233.46073
[2] Bratteli, O., Inductive limits of finite dimensional \(C^∗\)-algebras, Trans. Amer. Math. Soc., 171, 195-234 (1972) · Zbl 0264.46057
[3] Brown, L. G., Stable isomorphism of hereditary subalgebras of \(C^∗\)-algebras, Pacific J. Math., 71, 335-348 (1977) · Zbl 0362.46042
[4] \( \textsc{J. Cuntz}^∗ Math. Scand. \); \( \textsc{J. Cuntz}^∗ Math. Scand. \) · Zbl 0372.46063
[5] \( \textsc{J. Cuntz}^∗\)Comm. Math. Phys.; \( \textsc{J. Cuntz}^∗\)Comm. Math. Phys. · Zbl 0399.46045
[6] \( \textsc{J. Cuntz}C^∗\); \( \textsc{J. Cuntz}C^∗\) · Zbl 0354.46043
[7] Cuntz, J., Non-commutative Haar measure and algebraic finiteness conditions for simple \(C^∗\)-algebras, (Proceedings of Operator Algebras and Their Applications in Mathematical Physics. Proceedings of Operator Algebras and Their Applications in Mathematical Physics, Marseille (June 1977)), in press · Zbl 0434.46039
[8] Dixmier, J., Les \(C^∗\)-algèbres et leurs représentations, (Cahiers Scientifiques, 29 (1964), Gauthier-Villars: Gauthier-Villars Paris) · Zbl 0152.32902
[9] Elliott, G. A., Derivations of matroid \(C^∗\)-algebras, II, Ann. of Math., 100, 407-422 (1974) · Zbl 0296.46062
[10] Elliott, G. A., On the classification of inductive limits of sequences of semi-simple finite-dimensional algebras, J. Algebra, 38, 29-44 (1976) · Zbl 0323.46063
[11] Goodearl, K. R.; Handelman, D., Rank functions and \(K_0\) of regular rings, J. Pure Appl. Algebra, 7, 195-216 (1976) · Zbl 0321.16009
[12] Kadison, R. V., On the additivity of the trace in finite factors, (Proc. Nat. Acad. Sci. USA, 41 (1955)), 385-387 · Zbl 0064.36604
[13] Kadison, R. V.; Pedersen, G. K., Equivalence in operator algebras, Math. Scand., 27, 205-222 (1970) · Zbl 0217.16804
[14] Lance, E. C., On nuclear \(C^∗\)-algebras, J. Functional Analysis, 12, 157-176 (1973) · Zbl 0252.46065
[15] Laursen, K. B.; Sinclair, A. M., Lifting matrix units in \(C^∗\)-algebras, II, Math. Scand., 37, 167-172 (1975) · Zbl 0318.46073
[16] Murray, F. J.; von Neumann, J., On rings of operators, Ann. of Math., 37, 116-229 (1936) · Zbl 0014.16101
[17] Pedersen, G. K., Measure theory for \(C^∗\)-algebras, Math. Scand., 19, 131-145 (1966) · Zbl 0177.17701
[18] Pedersen, G. K., A decomposition theorem for \(C^∗\)-algebras, Math. Scand., 22, 266-268 (1968) · Zbl 0181.14303
[19] Pedersen, G. K., Measure theory for \(C^∗\)-algebras, III, Math. Scand., 25, 71-93 (1969) · Zbl 0189.44504
[20] Pedersen, G. K., The trace in semi-finite von Neumann algebras, Math. Scand., 37, 142-144 (1975) · Zbl 0323.46062
[21] Pedersen, G. K.; Petersen, N. H., Ideals in a \(C^∗\)-algebra, Math. Scand., 27, 193-204 (1970) · Zbl 0218.46056
[22] Pedersen, G. K.; Størmer, E.; Størmer, E., Automorphisms and equivalence in von Neumann algebras, II, Indiana Univ. Math. J., 23, 121-129 (1973) · Zbl 0258.46053
[23] Powers, R. T., Simplicity of the \(C^∗\)-algebra associated with the free group on two generators, Duke Math. J, 42, 151-156 (1975) · Zbl 0342.46046
[24] Sakai, S., \(C^∗\)-Algebras and \(W^∗\)-Algebras, (Ergebn. Math. Grenzgeb., 60 (1971), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 1024.46001
[25] Sakai, S., Derivations of simple \(C^∗\)-algebras, III, Tôhoku Math. J, 23, 559-564 (1971) · Zbl 0233.46074
[26] Størmer, E., Automorphisms and equivalence in von Neumann algebras, Pacific J. Math, 44, 371-383 (1973) · Zbl 0241.46060
[27] Takesaki, M., On the cross-norm of the direct product of \(C^∗\)-algebras, Tôhoku Math. J, 16, 111-122 (1964) · Zbl 0127.07302
[28] Thoma, E., Über unitäre Darstellungen abzählbarer diskreter Gruppen, math. Ann., 153, 111-138 (1964) · Zbl 0136.11603
[29] Yeadon, F. J., A new proof of the existence of a trace in a finite von Neumann algebra, Bull. Amer. Math. Soc., 77, 257-260 (1971) · Zbl 0241.46057
[30] Blackadar, B., Traces on Simple AF \(C^∗\)-Algebras (1979), Preprint, Reno
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