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Quasi-standard C*-algebras

Published online by Cambridge University Press:  24 October 2008

R. J. Archbold  and
D. W. B. Somerset
R. J. Archbold
Affiliation:
Department of Mathematical Sciences, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY
D. W. B. Somerset
Affiliation:
Queen's College, Oxford OX1 4AW
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Abstact

A necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 349 - 360
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Anderson, J. and Paschke, W.. The rotation algebra. Houston J. Math. 15 (1989), 1–26.Google Scholar
[2]Archbold, R. J.. Prime C*-algebras and antilattices. Proc. London Math. Soc. (3) 24 (1972), 669–680.CrossRefGoogle Scholar
[3]Archbold, R. J.. Topologies for primal ideals. J. London Math. Soc. (2) 36 (1987), 524–542.CrossRefGoogle Scholar
[4]Archbold, R. J. and Batty, C. J. K.. On factorial states of operator algebras, III. J. Operator Theory 15 (1986), 53–81.Google Scholar
[5]Blackadar, B.. Comparison theory for simple C*-algebras. In Operator Algebras and Applications, vol. 1, London Math. Soc. Lecture Note Ser. no. 135 (Cambridge University Press, 1988), pp. 21–54.Google Scholar
[6]Ching, W.-M.. The structure of standard C*-algebras and their representations. Pacific J. Math. 67 (1976), 131–153.CrossRefGoogle Scholar
[7]Cuntz, J.. The internal structure of simple C*-algebras. Proc. Sympos. Pure Math. 38, Part 1, 85–115 (American Mathematical Society, 1981).Google Scholar
[8]Dauns, J.. The primitive ideal space of a C*-algebra. Canad. J. Math. 26 (1974), 42–49.CrossRefGoogle Scholar
[9]Dauns, J. and Hofmann, K. H.. Representations of Rings by Continuous Sections. Memoirs Amer. Math. Soc. 83 (American Mathematical Society, 1968).Google Scholar
[10]Delaroche, C.. Sur les centres des C*-algèbres, II. Bull. Sci. Math. (2) 92 (1968), 111–128.Google Scholar
[11]Dixmier, J.. Sur les C*-algebres. Bull. Soc. Math. France 88 (1960), 95–112.CrossRefGoogle Scholar
[12]Dixmier, J.. Points séparés dans le spectre d'une C*-algèbre. Acta Sci. Math. (Szeged) 22 (1961), 115–128.Google Scholar
[13]Dixmier, J.. Les C*-algèbres et leurs Representations, 2nd edition (Gauthier Villars, 1969).Google Scholar
[14]Fell, J. M. G.. The structure of algebras of operator fields. Acta Math. 106 (1961), 233–280.CrossRefGoogle Scholar
[15]Gillman, L. and Jerison, M.. Rings of Continuous Functions (Van Nostrand, 1960).CrossRefGoogle Scholar
[16]Glimm, J. G.. A Stone–Weierstrass theorem for C*-algebras. Ann. of Math. 72 (1960), 216–244.CrossRefGoogle Scholar
[17]Kaplansky, I.. The structure of certain operator algebras. Trans. Amer. Math. Soc. 70 (1951), 219–255.CrossRefGoogle Scholar
[18]Lee, R.-Y.. On the C*-algebras of operator fields. Indiana Univ. Math. J. 25 (1976), 303–314.CrossRefGoogle Scholar
[19]Lee, R-Y.. Full algebras of operator fields trivial except at one point. Indiana Univ. Math. J. 26 1977, 351–372.CrossRefGoogle Scholar
[20]Misonou, Y.. On a weakly central operator algebra. Tohoku Math. J. 4 (1952), 194–202.CrossRefGoogle Scholar
[21]VV, D.. Somerset, B.. Quasi-standard C*-algebras and norms of inner derivations. D.Phil. thesis, Oxford University (1989).Google Scholar
[22]Tomiyama, J.. Topological representations of C*-algebras. Tohoku Math. J. 15 (1963), 96–102.Google Scholar
[23]Vesterstrom, J.. On open maps, compact convex sets, and operator algebras. J. London Math. Soc. (2) 6 (1973), 289–297.CrossRefGoogle Scholar